René L. Schilling

René L. Schilling's AcademicInfluence.com Rankings

René L. Schilling

Mathematics

#7489

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#10176

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Probability Theory

#124

World Rank

#151

Historical Rank

Statistics

#869

World Rank

#961

Historical Rank

Measure Theory

#2216

World Rank

#2664

Historical Rank

mathematics Degrees

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Mathematics

René L. Schilling's Degrees

PhD Mathematics University of Münster

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René L. Schilling's Published Works

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Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Financial Modelling with Jump Processes (2005) (1745)
Bernstein Functions: Theory and Applications (2010) (454)
Lévy-type processes : construction, approximation and sample path properties (2013) (196)
Growth and Hölder conditions for the sample paths of Feller processes (1998) (180)
A note on the existence of transition probability densities of Lévy processes (2010) (108)
Lévy Matters III (2013) (105)
Brownian Motion: An Introduction to Stochastic Processes (2012) (104)
Conservativeness and Extensions of Feller Semigroups (1998) (94)
Weak Order for the Discretization of the Stochastic Heat Equation Driven by Impulsive Noise (2009) (94)
Measures, Integrals and Martingales (2006) (93)
The Symbol Associated with the Solution of a Stochastic Differential Equation (2009) (90)
Coupling property and gradient estimates of L\'{e}vy processes via the symbol (2010) (82)
Levy-Type Processes and Pseudodifferential Operators (2001) (78)
Function spaces related to continuous negative definite functions: ψ-Bessel potential spaces (2001) (77)
Spatial Besov Regularity for Stochastic Partial Differential Equations on Lipschitz Domains (2010) (74)
Subordination in the sense of Bochner and a related functional calculus (1998) (73)
Stochastic calculus for uncoupled continuous-time random walks. (2008) (69)
Correlation Structure of Time-Changed Lévy Processes (2014) (61)
Asymptotic properties of Brownian motion delayed by inverse subordinators (2013) (60)
On the Feller property of Dirichlet forms generated by pseudo differential operators (2007) (52)
Adaptive Wavelet Methods for Elliptic Stochastic Partial Differential Equations (49)
Transition Density Estimates for a Class of Lévy and Lévy-Type Processes (2009) (49)
Some theorems on Feller processes: transience, local times and ultracontractivity (2011) (45)
Feller Processes Generated by Pseudo-Differential Operators: On the Hausdorff Dimension of Their Sample Paths (1998) (40)
Some Dirichlet spaces obtained by subordinate reflected diffusions (1999) (39)
On shift Harnack inequalities for subordinate semigroups and moment estimates for Lévy processes (2014) (39)
Strong Feller Continuity of Feller Processes and Semigroups (2010) (38)
On the coupling property of Lévy processes (2010) (37)
APPROXIMATION OF FELLER PROCESSES BY MARKOV CHAINS WITH LÉVY INCREMENTS (2009) (37)
From Lévy-Type Processes to Parabolic SPDEs (2016) (37)
Feller semigroups, Lp -sub-Markovian semigroups, and applications to pseudo-differential operators with negative definite symbols (2001) (36)
Measures, Integrals and Martingales: Frontmatter (2005) (36)
Stochastic solutions for fractional wave equations (2015) (35)
Weak convergence of finite element approximations of linear stochastic evolution equations with additive noise (2011) (35)
On the domain of fractional Laplacians and related generators of Feller processes (2016) (34)
Constructions of coupling processes for Lévy processes (2010) (33)
Distance multivariance: New dependence measures for random vectors (2017) (33)
From Schoenberg to Pick–Nevanlinna: Toward a complete picture of the variogram class (2008) (33)
A geometric interpretation of the transition density of a symmetric Lévy process (2011) (33)
Strong convergence of the Euler–Maruyama approximation for a class of Lévy-driven SDEs (2017) (32)
On Feller processes with sample paths in Besov spaces (1997) (32)
On the convergence analysis of Rothe ’ s method (32)
Reflected Spectrally Negative Stable Processes and their Governing Equations (2013) (31)
Lower bounded semi-Dirichlet forms associated with Lévy type operators (2011) (29)
Measures, Integrals and Martingales: Martingales (2005) (29)
LAGRANGIAN AND HAMILTONIAN FEYNMAN FORMULAE FOR SOME FELLER SEMIGROUPS AND THEIR PERTURBATIONS (2012) (28)
Age and gender-dependent bone density changes of the human skull disclosed by high-resolution flat-panel computed tomography (2011) (27)
Functional inequalities and subordination: stability of Nash and Poincaré inequalities (2011) (25)
Function Spaces as Dirichlet Spaces (About a Paper by Maz'ya and Nagel) (2005) (25)
On the coupling property and the Liouville theorem for Ornstein–Uhlenbeck processes (2011) (25)
Function Spaces as Path Spaces of Feller Processes (2000) (25)
Towards an Lp Potential Theory for Sub–Markovian Semigroups: Kernels and Capacities (2006) (24)
Conservativeness of Semigroups Generated by Pseudo Differntial Operators (1998) (24)
Fractals and chaos. The Mandelbrot set and beyond, by Benoit B. Mandelbrot. Pp. 308. £38.50. 2004, ISBN 0 387 20158 0 (Springer-Verlag). (2005) (22)
On the domain of the generator of a subordinate semigroup (1996) (22)
Subordination in the Sense of S. Bochner-An Approach through Pseudo Differential Operators (1996) (21)
Subgeometric rates of convergence for Markov processes under subordination (2015) (19)
Dirichlet operators and the positive maximum principle (2001) (19)
Sample Path Properties (2013) (17)
Detecting independence of random vectors: generalized distance covariance and Gaussian covariance (2017) (17)
On the Structure of the Domain of a Symmetric Jump-type Dirichlet Form (2012) (17)
High-resolution flat-panel volumetric CT images show no correlation between human age and sagittal suture obliteration--independent of sex. (2010) (16)
Stochastic differential equations: An introduction with applications (6th edn), by Bernt Oksendal. Pp. 360. £27. 2004. ISBN 3 540 04758 1 (Springer-Verlag). (2005) (16)
Feynman formulae for Feller semigroups (2010) (16)
Adaptive wavelet methods for the stochastic Poisson equation (2012) (16)
An Introduction to Lévy and Feller Processes. Advanced Courses in Mathematics - CRM Barcelona 2014 (2016) (16)
Morphological development and neurochemical differentiation of cerebellar inhibitory interneurons in microexplant cultures (2003) (15)
Toward an Efficient and Integrative Analysis of Limited-Choice Behavioral Experiments (2012) (14)
Construction and heat kernel estimates of general stable-like Markov processes (2020) (14)
Packing dimension profiles and Lévy processes (2011) (14)
Itô and Stratonovich integrals on compound renewal processes: the normal/Poisson case (2010) (13)
Transience and Non-explosion of Certain Stochastic Newtonian Systems (2002) (13)
Convergence Analysis of Spatially Adaptive Rothe Methods (2014) (13)
Lower bounds of the Hausdorff dimension for the images of Feller processes (2015) (12)
Feynman formulas and path integrals for some evolution semigroups related to τ-quantization (2011) (12)
Validity of covariance models for the analysis of geographical variation (2013) (12)
A unified approach to coupling SDEs driven by Lévy noise and some applications (2018) (11)
Progressive intrinsic ultracontractivity and heat kernel estimates for non-local Schrödinger operators (2019) (11)
Selected Papers I (2015) (11)
Estimates for multiple stochastic integrals and stochastic Hamilton-Jacobi equations (2004) (11)
On the small-time behaviour of L\'evy-type processes (2013) (10)
Fractional Derivatives Non-Symmetric and Time-Dependent Dirichlet Forms and the Drift Form (2000) (10)
Exact asymptotic formulas for the heat kernels of space and time-fractional equations (2018) (9)
Hamiltonian Feynman-Kac and Feynman Formulae for Dynamics of Particles with Position-Dependent Mass (2011) (9)
A probabilistic proof of Schoenberg's theorem (2018) (9)
On the coupling property and the Liouville theorem for Ornstein–Uhlenbeck processes (2011) (9)
Convolution inequalities for Besov and Triebel–Lizorkin spaces, and applications to convolution semigroups (2021) (8)
Comparable processes and the Hausdorff dimension of their sample paths (1996) (7)
Homogenization of Symmetric Lévy Processes on R d (2018) (7)
Detecting independence of random vectors II. Distance multivariance and Gaussian multivariance (2017) (7)
Harnack Inequalities for SDEs Driven by Time-Changed Fractional Brownian Motions (2016) (6)
Chapter 3. Bernstein functions (2012) (6)
Absolute continuity and singularity of probability measures induced by a purely discontinuous Girsanov transform of a stable process (2014) (5)
Adaptive Wavelet Methods for SPDEs (2014) (5)
A Probabilistic Inequality Related to Negative Definite Functions (2012) (5)
On a Poincaré-type Inequality for Energy Forms in Lp (2007) (5)
On a Cameron–Martin Type Quasi-Invariance Theorem and Applications to Subordinate Brownian Motion (2015) (4)
A Primer on Feller Semigroups and Feller Processes (2013) (4)
Homogenization of Symmetric Lévy Processes on $\mathbb{R}^d$ (2018) (4)
Stationary Distributions for Jump Processes with Inert Drift (2010) (4)
Approximation of the invariant measure of stable SDEs by an Euler--Maruyama scheme (2022) (4)
On level and collision sets of some Feller processes (2014) (4)
Bochner's subordination and fractional caloric smoothing in Besov and Triebel–Lizorkin spaces (2022) (3)
Measures, Integrals and Martingales: Measures (2005) (3)
Stationary distributions for jump processes with memory (2010) (3)
On the Convergence Analysis of the Inexact Linearly Implicit Euler Scheme for a Class of Stochastic Partial Differential Equations (2015) (3)
Continuity Assumptions in Cake-Cutting (2016) (3)
Counterexamples in Measure and Integration (3)
On the Liouville property for non-local L\'evy generators (2019) (2)
Lévy Processes, Generalized Moments and Uniform Integrability (2021) (2)
Functional inequalities and subordination: stability of Nash and Poincaré inequalities (2011) (2)
Communications and control (2021) (1)
Reflected stable subordinators for fractional Cauchy problems (2013) (1)
Dirichlet forms generated by pseudo differential operators : on the Feller property of the associated stochastic processes (2010) (1)
Markov Chain Approximation of Pure Jump Processes (2016) (1)
Brownian Motion (2021) (1)
Addendum to “From Schoenberg to Pick–Nevanlinna: Towards a complete picture of the variogram class” (2013) (1)
On the convergence analysis of the inexact linearly implicit Euler scheme for a class of SPDEs (2015) (1)
Subgeometric rates of convergence for Markov processes under subordination - Correction (2018) (1)
The Liouville theorem for a class of Fourier multipliers and its connection to coupling (2022) (1)
Measures, Integrals and Martingales: Hilbert space h (2005) (1)
L\'evy Processes, Martingales and Uniform Integrability (2021) (1)
Measures, Integrals and Martingales: The volume of a parallelepiped (2005) (1)
The Generator of a Lévy Process (2016) (1)
Extended L p Dirichlet Spaces (2010) (1)
Moderate Deviations and Strassen’s Law for Additive Processes (2014) (1)
Singular integrals of subordinators with applications to structural properties of SPDEs (2020) (1)
Maximal inequalities and some applications (2022) (1)
Analytical and Computational Problems Related to Fractional Gaussian Noise (2022) (1)
On q-scale functions of spectrally negative Lévy processes (2021) (1)
Large deviations for stochastic systems of slow-fast diffusions with non-Gaussian L\'evy noises. (2019) (1)
Complete Bernstein functions and subordinators with nested ranges. A note on a paper by P. Marchal (2016) (1)
Chapter 14. Stochastic integrals: L2-Theory (2012) (0)
Chapter 16. Itô’s formula (2012) (0)
I Integral Equations and Operator Theory (1999) (0)
15 Examples of complete Bernstein functions (2009) (0)
Measures, Integrals and Martingales: Orthonormal systems and their convergence behaviour (2005) (0)
Chapter 7. Brownian motion and transition semigroups (2012) (0)
Measures, Integrals and Martingales: Existence of measures (2005) (0)
Chapter 15. Stochastic integrals: beyond L2T (2012) (0)
Chapter 12. The spectral theorem and operator monotonicity (2012) (0)
Upper and lower bounds for stochastic processes, modern methods and classical problems by Michel Talagrand, pp. 626, £99.00 (hard), ISBN 978-3-642-54074-5, also available as e-book, Springer Verlag (2014). (2016) (0)
Chapter 2. Brownian motion as a Gaussian process (2012) (0)
Reviews - The Oxford handbook of random matrix theory , Gernot Akemann, Jinho Baik, Philippe Di Francesco (eds) Pp. 919. £110. 2011. ISBN: 978-0-19-957400-1 (Oxford University Press). (2013) (0)
19. Stochastic differential equations (2014) (0)
4 Positive and negative definite functions (2009) (0)
William Feller. A Biography (2015) (0)
Selected Papers II (2015) (0)
Chapter 1. Robert Brown’s new thing (2012) (0)
18. Applications of Itô’s formula (2014) (0)
Measures, Integrals and Martingales: Integrals of measurable functions and null sets (2005) (0)
Measures, Integrals and Martingales: Further reading (2005) (0)
Some Dirichlet spaces obtained by subordinate re ected di usions (2001) (0)
3. Constructions of Brownian motion (2014) (0)
Chapter 8. The PDE connection (2012) (0)
1 Completely monotone functions (2009) (0)
5. Brownian motion as a martingale (2014) (0)
10 Special Bernstein functions and potentials (2009) (0)
Chapter 13. Subordination and Bochner’s functional calculus (2012) (0)
Calculus of variations by Filip Rindler, pp. 444, £39.99 (paper), ISBN 978-3-319-77636-1, also available as e-book, Springer Verlag (2018) (2020) (0)
A geometric interpretation of the transition density of a symmetric Lévy process (2012) (0)
13. Strassen’s functional law of the iterated logarithm (2014) (0)
Index of notation (2012) (0)
A Digression: Semigroups (2016) (0)
Cutting a Cake Is Not Always a "Piece of Cake": A Closer Look at the Foundations of Cake-Cutting Through the Lens of Measure Theory (2021) (0)
Construction of Lévy Processes (2016) (0)
Solution Manual (2020) (0)
Chapter 1. Laplace transforms and completely monotone functions (2012) (0)
2. Brownian motion as a Gaussian process (2014) (0)
Measures, Integrals and Martingales: Uniqueness of measures (2005) (0)
Stochastic integration for uncoupled continuous-time random walks (2008) (0)
Real analysis. Measure theory, integration and Hilbert spaces , by Elias M. Stein and Rami Shakarchi. Pp.402. £38.95. 2005. ISBN 0 691 11386 6 (Princeton University Press). (2007) (0)
Some facts from point-set topology (2005) (0)
7 Complete Bernstein functions: properties (2009) (0)
20. Stratonovich’s stochastic calculus (2014) (0)
Chapter 13. Skorokhod representation (2012) (0)
13 Riemann vs. Lebesgue (2015) (0)
Measures, Integrals and Martingales: Dependence chart (2005) (0)
Asymptotic behaviour and functional limit theorems for a time changed Wiener process (2020) (0)
Measures, Integrals and Martingales: lim inf and lim sup (2005) (0)
On the Markov Property (2016) (0)
From Lévy to Feller Processes (2016) (0)
PR ] 1 A ug 2 01 8 A probabilistic proof of Schoenberg ’ s theorem (2018) (0)
Measures, Integrals and Martingales: Product measures and Fubini's theorem (2005) (0)
5 A probabilistic intermezzo (2009) (0)
A journey through statistical physics. From foundations to the quantum Hall effect: Selecta of Jürg Fröhlich . Giovanni Felder, Gian Michele Graf, Klaus Hepp (eds). Pp. 857. £126.00. 2009. ISBN: 13-978-1-4020-8886-5 (Springer). (2010) (0)
Measures, Integrals and Martingales: σ-algebras (2005) (0)
For which functions are $f(X_t)-\mathbb{E} f(X_t)$ and $g(X_t)/\mathbb{E} g(X_t)$ martingales? (2021) (0)
Chapter 17. Applications of Itô’s formula (2012) (0)
Transformations of Feller Processes (2013) (0)
22. Simulation of Brownian motion by Björn Böttcher (2014) (0)
Corrigendum to “Constructions of coupling processes for Lévy processes” (2011) (0)
Adaptive wavelet methods for the stochastic Poisson equation (2012) (0)
Chapter 4. The canonical model (2012) (0)
Convergence Analysis of Spatially Adaptive Rothe Methods (2014) (0)
Chapter 6. Complete Bernstein functions (2012) (0)
11. Brownian motion as a random fractal (2014) (0)
6 Complete Bernstein functions: representation (2009) (0)
Weak Order for the Discretization of the Stochastic Heat Equation Driven by Impulsive Noise (2012) (0)
Measures, Integrals and Martingales: The pleasures of counting (2005) (0)
Chapter 6. Brownian motion as a Markov process (2012) (0)
Chapter 16. Examples of complete Bernstein functions (2012) (0)
Chapter 18. Stochastic differential equations (2012) (0)
The Bismut-Elworthy-Li Formula and Gradient Estimates for Stochastic Differential Equations (2016) (0)
Continuous-Time Random Walks, Fractional Calculus and Stochastic Integrals (2009) (0)
Measures, Integrals and Martingales: Integrals of images and Jacobi's transformation rule (2005) (0)
Chapter 19. On diffusions (2012) (0)
Mathematical constants II by Steven R. Finch, pp. 769, £125 (hard), ISBN 978-1-10847-059-9, Cambridge University Press (2018) (2021) (0)
Measures, Integrals and Martingales: Measurable functions (2005) (0)
3 Bernstein functions (2009) (0)
Moderate Deviations and Strassen’s Law for Additive Processes (2014) (0)
Measures, Integrals and Martingales: The Radon–Nikodým theorem and other applications of martingales (2005) (0)
Measures, Integrals and Martingales: A summary of the Riemann integral (2005) (0)
Chapter 14. Potential theory of subordinate killed Brownian motion (2012) (0)
14. Skorokhod representation (2014) (0)
Reviews (2013) (0)
Measures, Integrals and Martingales: Convergence theorems and their applications (2005) (0)
12. The growth of Brownian paths (2014) (0)
Chapter 10. Regularity of Brownian paths (2012) (0)
9 A second probabilistic intermezzo (2009) (0)
Chapter 9. A second probabilistic intermezzo (2012) (0)
Measures, Integrals and Martingales: References (2005) (0)
Chapter 5. A probabilistic intermezzo (2012) (0)
Chapter 8. Thorin–Bernstein functions (2012) (0)
Measures, Integrals and Martingales: Inner product spaces (2005) (0)
2 Sigma-Algebren (2015) (0)
Chapter 5 Adaptive Wavelet Methods for SPDEs (2014) (0)
Construction of Feller Processes (2013) (0)
Measures, Integrals and Martingales: Measurable mappings (2005) (0)
Measures, Integrals and Martingales: Integrals with respect to image measures (2005) (0)
16. Stochastic integrals: beyond L2T (2014) (0)
A Digression: Stochastic Integrals (2016) (0)
A Probabilistic proof of the breakdown of Besov regularity in $L$-shaped domains (2016) (0)
4. The canonical model (2014) (0)
Chapter 15. Applications to generalized diffusions (2012) (0)
Chapter 10. Transformations of Bernstein functions (2012) (0)
On the Convergence Analysis of the Inexact Linearly Implicit Euler Scheme for a Class of Stochastic Partial Differential Equations (2016) (0)
10. Regularity of Brownian paths (2014) (0)
Quasi-ergodicity of compact strong Feller semigroups on $L^2$ (2023) (0)
1. Robert Brown’s new thing (2014) (0)
Transition Density Estimates for a Class of Lévy and Lévy-Type Processes (2010) (0)
Inner and Outer Measure (2021) (0)
Chapter 7. Properties of complete Bernstein functions (2012) (0)
The (strong) Liouville property for a class of non-local operators (2021) (0)
Stochastic solutions for fractional wave equations (2014) (0)
Two Special Lévy Processes (2016) (0)
Bourbaki, Nicolas: Integration I (Chapters 1-6) and II (Chapters 7-9) . 2 volumes. Pp. 472 and 326. £77.00 each. 2004. ISBN 0 540 41129 1 and 0 540 20585 3 (Springer-Verlag). (2005) (0)
Wasserstein-$1$ distance between SDEs driven by Brownian motion and stable processes (2023) (0)
14 Applications to generalized diffusions (2009) (0)
Non-measurable sets (2005) (0)
8 Thorin–Bernstein functions (2009) (0)
Chapter 5. Brownian motion as a martingale (2012) (0)
Markov Chain Approximation of Pure Jump Processes (2018) (0)
6. Brownian motion as a Markov process (2014) (0)
7. Brownian motion and transition semigroups (2014) (0)
A course on integration theory by Nicolas Lerner, pp. 492, £62.99 (paper), ISBN 978-3-0348-0693-0, also available as e-book, Birkhäuser (2014). (2016) (0)
Homogenization of Symmetric L\'evy Processes on $\mathbb{R}^d$ (2018) (0)
11 The spectral theorem and operator monotonicity (2009) (0)
Chapter 12. Strassen’s Functional Law of the Iterated Logarithm (2012) (0)
An Inequality Related to Negative Definite Functions (2012) (0)
Lower Bounds of the Hausdorff dimension for Feller processes (2014) (0)
Symbols and Semimartingales (2016) (0)
Measures, Integrals and Martingales: Martingale convergence theorems (2005) (0)
17 Itô’s formula (2014) (0)
An analytic proof of the Lévy--Khinchin formula on $\mathbb{R}^n$ (1998) (0)
Measures, Integrals and Martingales: Conditional expectations in L 2 (2005) (0)
15. Stochastic integrals: L2-Theory (2014) (0)
Measures, Integrals and Martingales: Prologue (2005) (0)
Chapter 11. The growth of Brownian paths (2012) (0)
Chapter 4. Positive and negative definite functions (2012) (0)
A ug 2 01 9 Large deviations for stochastic systems of slow-fast diffusions with non-Gaussian Lévy noises ✩ (2019) (0)
Measures, Integrals and Martingales: Integration of positive functions (2005) (0)
13 Potential theory of subordinate killed Brownian motion (2009) (0)
8. The PDE connection (2014) (0)
Bochner's Subordionation and Fractional Caloric Smoothing in Besov and Triebel--Lizorkin Spaces. (2019) (0)
Measures, Integrals and Martingales: The function spaces Lp , 1 ≤ p ≤ ∞ (2005) (0)
Measures, Integrals and Martingales: Uniform integrability and Vitali's convergence theorem (2005) (0)
Chapter 9. The variation of Brownian paths (2012) (0)
Minkowski's Inequality for Integrals (2008) (0)
12 Subordination and Bochner’s functional calculus (2009) (0)
Chapter 11. Special Bernstein functions and potentials (2012) (0)
9. The variation of Brownian paths (2014) (0)
MFO-RIMS Tandem Workshop: Nonlocality in Analysis, Probability and Statistics (2023) (0)
Chapter 3. Constructions of Brownian motion (2012) (0)
Measure and integration: Publications 1997-2011 by Heinz König, pp 512, £85.50, $129.00, €101.60, ISBN 978-3-0348-0381-6, Birkhäuser (2012). (2014) (0)
Feller Generators and Symbols (2013) (0)
Editorial: Math. Nachr. 1/2009 (2009) (0)

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TU Dresden

René L. Schilling's Academic­Influence.com Rankings

René L. Schilling's Degrees

Why Is René L. Schilling Influential?

René L. Schilling's Published Works

Published Works

What Schools Are Affiliated With René L. Schilling?

René L. Schilling's AcademicInfluence.com Rankings