René L. Schilling
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Mathematics
René L. Schilling's Degrees
- PhD Mathematics University of Münster
Why Is René L. Schilling Influential?
(Suggest an Edit or Addition)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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