Daniel W. Stroock | Academic Influence

Daniel W. Stroock's AcademicInfluence.com Rankings

Daniel W. Stroock

Mathematics

#632

World Rank

#1176

Historical Rank

#279

USA Rank

Measure Theory

#490

World Rank

#696

Historical Rank

#203

USA Rank

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Mathematics

Daniel W. Stroock's Degrees

PhD Mathematics University of California, Berkeley
Bachelors Mathematics University of California, Berkeley

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Why Is Daniel W. Stroock Influential?

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According to Wikipedia, Daniel Wyler Stroock is an American mathematician, a probabilist. He is regarded and revered as one of the fundamental contributors to Malliavin calculus with Shigeo Kusuoka and the theory of diffusion processes with S. R. Srinivasa Varadhan with an orientation towards the refinement and further development of Itô’s stochastic calculus.

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Daniel W. Stroock's Published Works

Number of citations in a given year to any of this author's works

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

Geometric Bounds for Eigenvalues of Markov Chains (1991) (930)
On the Support of Diffusion Processes with Applications to the Strong Maximum Principle (1972) (568)
Upper bounds for symmetric Markov transition functions (1986) (461)
Applications of the Malliavin calculus. II (1985) (423)
An Introduction to the Theory of Large Deviations (1984) (387)
Diffusion processes with continuous coefficients, I (1969) (372)
Diffusion processes associated with Lévy generators (1975) (336)
Diffusion processes with boundary conditions (1971) (334)
A new proof of Moser's parabolic harnack inequality using the old ideas of Nash (1986) (333)
Logarithmic Sobolev inequalities and stochastic Ising models (1987) (310)
Probability Theory, an Analytic View (1995) (256)
Diffusion semigroups corresponding to uniformly elliptic divergence form operators (1988) (213)
Generalized Ornstein-Uhlenbeck Processes and Infinite Particle Branching Brownian Motions (1978) (189)
The logarithmic sobolev inequality for discrete spin systems on a lattice (1992) (184)
The $L^p$-integrability of Green’s functions and fundamental solutions for elliptic and parabolic equations (1984) (178)
Asymptotics of the spectral gap with applications to the theory of simulated annealing (1989) (175)
On degenerate elliptic‐parabolic operators of second order and their associated diffusions (1972) (172)
An Introduction to the Analysis of Paths on a Riemannian Manifold (2005) (171)
The equivalence of the logarithmic Sobolev inequality and the Dobrushin-Shlosman mixing condition (1992) (159)
Simulated annealing via Sobolev inequalities (1988) (155)
An Introduction to Markov Processes (2004) (154)
The Malliavin calculus, a functional analytic approach (1981) (139)
A New Proof of Moser's Parabolic Harnack Inequality via the Old Ideas of Nash (127)
A probabilistic approach to (1974) (120)
Some stochastic processes which arise from a model of the motion of a bacterium (1974) (110)
Moment estimates derived from Poincar'e and log-arithmic Sobolev inequalities (1994) (110)
Diffusions on an infinite dimensional torus (1981) (95)
Some applications of stochastic calculus to partial differential equations (1983) (95)
Long time estimates for the heat kernel associated with a uniformly subelliptic symmetric second order operator (1988) (91)
The logarithmic Sobolev inequality for continuous spin systems on a lattice (1992) (89)
Markov processes from K. Itô's perspective (2003) (86)
Hypercontractivity and spectral gap of symmetric diffusions with applications to the stochastic ising models (1990) (84)
Markov chain approximations to symmetric diffusions (1997) (83)
Probability Theory: An Analytic View. (1995) (83)
Large deviations and stochastic flows of diffeomorphisms (1988) (77)
Towards a Riemannian Geometry on the Path Space over a Riemannian Manifold (1995) (76)
Homogeneous chaos revisited (1987) (76)
Short time behavior of the heat kernel and its logarithmic derivatives (1996) (75)
A concise introduction to the theory of integration (1990) (74)
Precise asymptotics of certain Wiener functionals (1991) (64)
Estimates on the Fundamental Solution to Heat Flows With Uniformly Elliptic Coefficients (1991) (56)
Nearest neighbor birth and death processes on the real line (1978) (56)
Some remarkable martingales (1981) (54)
Logarithmic Sobolev inequalities for gibbs states (1993) (54)
A Martingale Approach to Infinite Systems of Interacting Processes (1976) (53)
Upper bounds on derivatives of the logarithm of the heat kernel (1998) (51)
The malliavin calculus and its applications (1981) (51)
In one and two dimensions, every stationary measure for a stochastic Ising Model is a Gibbs state (1977) (50)
L2 theory for the stochastic Ising model (1976) (49)
Lectures on Topics in Stochastic Differential Equations (1983) (49)
Applications of the stochastic Ising model to the Gibbs states (1976) (49)
Central Limit Phenomena of Various Interacting Systems (1979) (49)
Rademacher's Theorem for Wiener Functionals (1993) (48)
Microcanonical distributions for lattice gases (1991) (47)
The partial malliavin calculus and its application to non-linear filtering (1984) (45)
Microcanonical Distributions, Gibbs States, and the Equivalence of Ensembles (1991) (42)
On the growth of stochastic integrals (1971) (40)
An example in the theory of hypercontractive semigroups (1985) (37)
On extremal solutions of martingale problems (1980) (37)
On certain systems of parabolic equations (1970) (35)
Uniform andL2 convergence in one dimensional stochastic Ising models (1989) (35)
Markov Processes from K. Ito's Perspective (AM-155) (2003) (34)
Essentials of Integration Theory for Analysis (2011) (33)
Lectures on Stochastic Analysis: Diffusion Theory (1987) (32)
The Poisson kernel for certain degenerate elliptic operators (1984) (31)
Dual processes and their application to infinite interacting systems (1979) (29)
The Fundamental Solution to the Wright-Fisher Equation (2010) (28)
On the ergodic properties of Glauber dynamics (1995) (28)
Some boundedness properties of certain stationary diffusion semigroups (1985) (27)
Lévy's area under conditioning (2006) (25)
An application of the Bakry-Emery criterion to infinite dimensional diffusions (1986) (23)
Partial Differential Equations for Probabilists (2008) (23)
An estimate on the Hessian of the heat kernel (1995) (23)
Pinned Brownian Motion and its Perturbations (1996) (21)
An approximation scheme for reflected stochastic differential equations (2010) (20)
Partial Differential Equations for Probabalists: Frontmatter (2008) (20)
LIMIT THEOREMS FOR RANDOM WALKS ON LIE GROUPS (2016) (20)
Short time behavior of logarithmic derivatives of the heat kernel (1997) (20)
On the Rate at Which a Homogeneous Diffusion Approaches a Limit, an Application of Large Deviation Theory to Certain Stochastic Integrals (1986) (20)
A simple PDE and Wiener‐Hopf Riccati equations (2005) (18)
The legacy of Norbert Wiener : a centennial symposium in honor of the 100th anniversary of Norbert Wiener's birth, October 8-14, 1994, Massachusetts Institute of Technology, Cambridge, Massachusetts (1997) (18)
Review: I. I. Gihman and A. V. Skorohod, The theory of stochastic processes (1980) (18)
Estimates on the heat kernel for second order divergence form operators (1992) (18)
Asymptotics of certain wiener functionals with degenerate extrema (1994) (18)
The kac approach to potential theory, II (1967) (18)
Applications of fefferman‐stein type interpolation to probability theory and analysis (1973) (17)
The Malliavin calculus and its application to second order parabolic differential equations: Part I (2005) (17)
Abstract Wiener space, revisited (2008) (17)
Integration by parts for pinned Brownian motion (1995) (13)
A Hodge theory for some non-compact manifolds (2000) (13)
The Malliavin calculus and its application to second order parabolic differential equations: Part II (1981) (13)
Gaussian measures in traditional and not so traditional settings (1996) (12)
Kiyosi Itô selected papers (1987) (12)
Further study of a simple {PDE} (2006) (12)
Generalized ornstein — Uhlenbeck processes as limits of interacting systems (1981) (11)
A Probabilistic Approach to H p (R d ) (1974) (11)
Diffusions as Integral Curves, or Stratonovich without Itô (1994) (11)
Mathematics of Probability (2013) (10)
On the spectrum of Markov semigroups and the existence of invariant measures (1982) (10)
Groups and Analysis: Weyl's Lemma, one of many (2008) (9)
Variations On A Theme By Bismut (1996) (8)
A characterization of harmonic measure and Markov processes whose hitting distributions are preserved by rotations translations and dilatations (1982) (8)
The D.L.R. conditions for translation invariant Gaussian measures on L(Rd) (1980) (8)
Elements of Stochastic Calculus and Analysis (2018) (7)
A peculiar two point boundary value problem (2007) (6)
An ergodic theorem for poisson processes on a compact group with applications to random evolutions (1974) (6)
Doing analysis by tossing a coin (2000) (6)
Anticipative diffusion and related change of measures (1993) (5)
A function space large deviation principle for certain stochastic integrals (1989) (5)
Non-divergence form operators and variations on Yau's explosion criterion (1998) (5)
Partial Differential Equations for Probabalists: References (2008) (5)
Partial Differential Equations for Probabalists: Preliminary Elliptic Regularity Results (2008) (5)
On a theorem of Laurent Schwartz (2011) (5)
Lectures on infinite interacting systems (1977) (4)
Microcanonical Distributions for one Dimensional Lattice Gases (1991) (4)
An introduction to analysis on path space (1999) (4)
Introduction to Large Deviations from Ergodic Phenomena (1984) (3)
Diffusion processes and martingales I (1971) (3)
Determinants, their applications to Markov processes, and a random walk proof of Kirchhoff's matrix tree theorem (2013) (3)
Maps that take Gaussian measures to Gaussian measures (2010) (3)
Precise asymptotics in large deviations (1993) (3)
Geometric bounds for the eigenvalues (2018) (3)
Additive Functions and Gaussian Measures (2013) (3)
Remarks on the HRT Conjecture (2015) (3)
Doeblin’s Theory for Markov Chains (2014) (2)
Group actions and singular martingales (2003) (2)
Remembering Paul Malliavin (2011) (2)
A highly unstable initial value boundary value problem (2008) (2)
Book Review: Dirichlet forms & symmetric Markov processes@@@Book Review: Dirichlet forms (1996) (2)
Some Riemann Sums Are Better Than Others (2008) (2)
Logarithmic Sobolev Inequalities (1984) (2)
Estimates for transition probabilities on a compact manifold (2007) (2)
On the Derivation of the Black-Scholes Formula (2005) (2)
Reversible Markov Processes (2014) (2)
Uniform large deviations (2001) (2)
Some comments on independent σ-algebras (1976) (2)
Elements of Complex Analysis (2015) (1)
On a Flow of Transformations of a Wiener Space (2011) (1)
Integral Functionals of Probability that Depend Only on Mean Values (2023) (1)
Lectures on infinite interacting systems (Lectures in mathematics, 11) (1978) (1)
Brownian motion on a submanifold (2004) (1)
Some thoughts about Segal's ergodic theorem (2010) (1)
Slepian's inequality and commuting semigroups (1987) (1)
Topics in probability theory : seminar 1971-1972 (1973) (1)
An exercise in Malliavin's calculus (2015) (1)
On a Manifold (2008) (1)
A Probabilistic Approach to Finding Estimates for the Heat Kernel Associated with a Hörmander Form Operator (1987) (1)
Gaussian Measures in Finite and Infinite Dimensions (2023) (1)
Theory of Diffusion Processes (2010) (1)
λπ-invariant measures (1983) (1)
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY Volume 79 , Number 4 , July 1973 ON A CONJECTURE OF (2007) (0)
Colloquium SOME THINGS THAT CAN HAPPEN WHEN THE MINIMUM PRINCIPLE FAILS (2008) (0)
Brownian motion in Euclidean space (2005) (0)
Wiener Measure and Partial Differential Equations (2010) (0)
Cramér’s Theorem (1984) (0)
Some continuous-time processes (2013) (0)
Chapter 4. Further Considerations (2003) (0)
On Taking Square Roots (2018) (0)
Erratum to: Solutions to Stochastic Differential Equations as a Function of the Starting Point (1981) (0)
Analysis on the Real Line (2015) (0)
Infinitely Divisible Laws (2010) (0)
Parabolic Partial Differential Equations (2006) (0)
Some Background Material for 18.176 (2016) (0)
The Trajectories of Solutions to Stochastic Differential Equations (1981) (0)
$\lambda_\pi$-invariant measures (1983) (0)
Kolmogorov’s Equations (2018) (0)
A resumé of some of the applications of Malliavin's calculus (1982) (0)
Perturbing Brownian paths (2005) (0)
Identification of the Rate Function (1984) (0)
The Stochastic Calculus of Diffusion Theory (2006) (0)
Stochastic processes and measures on function space (1987) (0)
Study of Simple but Challenging Diffusion Equation (2007) (0)
Chapter 2. Moving to Euclidean Space, the Real Thing (2003) (0)
On Taking Square Roots (2018) (0)
Continuous Parameter Martingales (2010) (0)
Paul Malliavin and the Journal of Functional Analysis (2008) (0)
Probability Theory: Sums of Independent Random Variables (2010) (0)
Integration in Higher Dimensions (2015) (0)
Radon–Nikodym, Hahn, Daniell, and Carathéodory (2020) (0)
Brownian Stochastic Integration (2018) (0)
Markov Processes, Regularity of Their Sample Paths, and the Wiener Measure (2006) (0)
Non-uniform results (2001) (0)
Wiener space , revisited (2018) (0)
Markov Processes in Continuous Time (2014) (0)
Random Walks and the Reflection Principle (2004) (0)
Local analysis of Brownian motion (2005) (0)
The Martingale Formulation (2006) (0)
Discrete parameter stochastic processes (2013) (0)
Lebesgue’s Measure (1994) (0)
Chapter 3. Itô's Approach in the Euclidean Setting (2003) (0)
Brownian Motion on a Submanifold 167 (2004) (0)
A Concise Introduction to Analysis (2015) (0)
The Non-unique Case (2006) (0)
Conditioning and Martingales (2010) (0)
Partial Differential Equations for Probabalists: Non-Elliptic Regularity Results (2008) (0)
Malliavin Calculus at Saint-Flour (2012) (0)
Some Extensions and Applications of Martingale Theory (2010) (0)
Chapter 8. Stratonovich's Theory (2003) (0)
Some intrinsic Riemannian geometry (2005) (0)
Some Basic Inequalities (1994) (0)
A remarkably interesting, simple P.D.E. (2006) (0)
More About the Ergodic Properties of Markov Chains (2014) (0)
Other Theories of Stochastic Integration (2018) (0)
WHEN DO RANDOM WALKS RETURN ? (2003) (0)
The bundle of orthonormal frames (2005) (0)
The Radon–Nikodym Theorem, Daniell Integration, and Carathéodory’s Extension Theorem (2011) (0)
Cauchy's functional equation and Gaussian measures (2019) (0)
Limit theorems and related problems - A. A. Borovkov. (1986) (0)
On a conjecture of M. Kac (1973) (0)
AMERICAN MATHElfaATICAL SOCIETY (1977) (0)
A Little Abstract Theory (1994) (0)
EUGENE BARRY FABES (1937-1997) (1998) (0)
Lectures on Stochastic Analysis: Diffusion Theory: Diffusions and martingales (1987) (0)
Hilbert Space and Elements of Fourier Analysis (2020) (0)
Changes of Variable (2020) (0)
Chapter 7. The Kunita-Watanabe Extension (2003) (0)
Doing it on a manifold, an extrinsic approach (2005) (0)
Some applications to probability theory (2013) (0)
Products of Measures (2020) (0)
Existence of a Rate Function (1984) (0)
A Little Bit of Analytic Function Theory (2015) (0)
BOOK REVIEW (2001) (0)
Lebesgue Integration (2020) (0)
Book reviews (1998) (0)
Book reviews (1986) (0)
Some addenda, extensions, and refinements (2005) (0)
Chapter 5. Itô's Theory of Stochastic Integration (2003) (0)
Preliminary Material: Extension Theorems, Martingales, and Compactness (2006) (0)
Partial Differential Equations for Probabalists: Kolmogorov's Forward, Basic Results (2008) (0)
The End of an Era (2004) (0)
The central limit theorem and Gaussian distributions (2013) (0)
Some Non-Uniform Large Deviation Results (1984) (0)
The Classical Theory (2020) (0)
Basic Inequalities and Lebesgue Spaces (2020) (0)
Brownian Motion in Small Time, Strassen’s Iterated Logarithm (1984) (0)
Probability theory on uncountable sample spaces (2013) (0)
Some Estimates on the Transition Probability Functions (2006) (0)
Birth of a Theorem—A Book Review by (2015) (0)
Itô’s Uniqueness and Uniqueness to the Martingale Problem (2006) (0)
Random Walks, a Good Place to Begin (2014) (0)
Essentials of intergration theory for analysis / Daniel W. Stroock (2011) (0)
Erratum to: The Trajectories of Solutions to Stochastic Differential Equations (1981) (0)
Daniel Stroock Interview undated (2010) (0)
General Cramér theory (2001) (0)
Large Deviations, Some Generalities (1984) (0)
Solutions to Stochastic Differential Equations as a Function of the Starting Point (1981) (0)
An Application of Gaussian Measures to Functional Analysis (2013) (0)
Lectures on Stochastic Analysis: Diffusion Theory: The martingale problem formulation of diffusion theory (1987) (0)
lecture notes for the period of concentration on Malliavin calculus and applications to partial differential equations (1986) (0)
Probability Theory: Some Classical Potential Theory (2010) (0)
The theory of stochastic processes, by I. I. Gihman and A. V. Skorohod, (2007) (0)
Some Comments about Itô's Construction Procedure (2004) (0)
Historical notes and references (2001) (0)
Lectures on Probability Theory - D. Bakry; R. D. Gill; S. A. Molchanov. (1998) (0)
Partial Differential Equations for Probabalists: Subelliptic Estimates and Hörmander's Theorem (2008) (0)
Chapter 1. Finite State Space, a Trial Run (2003) (0)
An exercise in Malliavins calculus (2015) (0)
Probability Theory: The Central Limit Theorem (2010) (0)
Chapter 6. Applications of Stochastic Integration to Brownian Motion (2003) (0)
More about extrinsic Riemannian geometry (2005) (0)
Gaussian Measures on a Banach Space (2010) (0)
Diffusions in Euclidean space (2005) (0)
A Minimal Introduction to Measure Theory (2014) (0)
Large Deviation Principle for Diffusions (1984) (0)
Probability Theory: Convergence of Measures on a Polish Space (2010) (0)
Some background and preliminaries (2013) (0)

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