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Diffusions, Markov processes, and martingales

Data up to Jan 2025

Published1979
Citations1,211
References210

Total Citations Per Year

Abstract

References (210)

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Functional analysis

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Multidimensional Diffusion Processes

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Statistical theory of turbulenc

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Stochastic Differential Equations and Applications

1976 • 1,469 citations

Principles of random walk

1964 • 1,469 citations

Geometric Integration Theory

1957 • 1,434 citations

Markov Processes and Potential Theory

2007 • 1,384 citations

Controlled Diffusion Processes

1980 • 1,343 citations

Markov Chains with Stationary Transition Probabilities.

1962 • 1,298 citations

Lectures on Choquet’s Theorem

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Functional Integration and Quantum Physics

1979 • 1,264 citations

Convergence of Random Processes and Limit Theorems in Probability Theory

1956 • 1,206 citations

Dynamical Theories of Brownian Motion

2020 • 1,180 citations

Diffusion Processes and their Sample Paths.

1968 • 1,163 citations

Calcul Stochastique et Problèmes de Martingales

1979 • 1,157 citations

Ergodic Theory and Information

1966 • 1,133 citations

Théorie de l'addition des variables aléatoires

1937 • 1,095 citations

Comparison Theorems in Riemannian Geometry

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Processus stochastiques et mouvement brownien

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Probabilités et potentiel

1966 • 946 citations

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1967 • 913 citations

11. The Imbedding Problem for Riemannian Manifolds

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Limit Theorems for Stochastic Processes

1956 • 898 citations

On the uniqueness of solutions of stochastic differential equations

1971 • 854 citations

Transversal mappings and flows

2008 • 840 citations

Distribution Function Inequalities for Martingales

1973 • 837 citations

Geometry of Manifolds

1964 • 822 citations

Dirichlet Forms and Markov Processes

1980 • 782 citations

Stochastic Filtering Theory

1980 • 769 citations

An innovations approach to least-squares estimation--Part I: Linear filtering in additive white noise

1968 • 759 citations

An invariance principle for the law of the iterated logarithm

1964 • 711 citations

Introduction to Potential Theory.

1971 • 672 citations

Subadditive Ergodic Theory

1973 • 657 citations

On Square Integrable Martingales

1967 • 633 citations

The theory of stochastic processes

1974 • 632 citations

Stochastic partial differential equations and filtering of diffusion processes

1980 • 588 citations

On the Support of Diffusion Processes with Applications to the Strong Maximum Principle

1972 • 562 citations

Brownian Motion and Classical Potential Theory

1978 • 495 citations

Stochastic integral

1944 • 494 citations

Capacités et processus stochastiques

1972 • 492 citations

The diffusion of shape

1977 • 471 citations

Approximate Integration of Stochastic Differential Equations

1975 • 467 citations

Sample Functions of Stochastic Processes with Stationary, Independent Increments.

1972 • 403 citations

A TRANSFORMATION OF THE PHASE SPACE OF A DIFFUSION PROCESS THAT REMOVES THE DRIFT

1974 • 400 citations

Stopping Times and Tightness. II

1989 • 386 citations

Bases mathématiques du calcul des probabilités

1964 • 383 citations

Stochastic differential equations for the non linear filtering problem

1972 • 380 citations

Un Cours sur les Intégrales Stochastiques

2002 • 375 citations

On the Gap Between Deterministic and Stochastic Ordinary Differential Equations

1978 • 369 citations

Ergodic Properties of Recurrent Diffusion Processes and Stabilization of the Solution to the Cauchy Problem for Parabolic Equations

1960 • 352 citations

Path Decomposition and Continuity of Local Time for One-Dimensional Diffusions, I

1974 • 351 citations

Some solvable stochastic control problemst†

1980 • 343 citations

Probabilities on Algebraic Structures.

1964 • 335 citations

Completely random measures

1967 • 335 citations

Semi-Martingales et Grossissement d’une Filtration

1980 • 332 citations

Diffusion processes with boundary conditions

1971 • 324 citations

Brownian Motion and Diffusion

1973 • 318 citations

Diffusion processes associated with L�vy generators

1975 • 317 citations

A comparison theorem for solutions of stochastic differential equations and its applications

1977 • 314 citations

EUCLIDEAN QUANTUM FIELD THEORY

1993 • 291 citations

A Real Variable Lemma and the Continuity of Paths of Some Gaussian Processes

1970 • 290 citations

Almost sure behavior of sums of independent random variables and martingales

1967 • 288 citations

Martingale inequalities: seminar notes on recent progress

1973 • 277 citations

Some Classes of Random Fields inn-Dimensional Space, Related to Stationary Random Processes

1957 • 270 citations

Markoff processes and potentials I

1957 • 253 citations

Minimal positive harmonic functions

1941 • 249 citations

Some Theorems Concerning 2-Dimensional Brownian Motion

1991 • 245 citations

First passage times and sojourn times for Brownian motion in space and the exact Hausdorff measure of the sample path

1962 • 245 citations

The Representation of Functionals of Brownian Motion by Stochastic Integrals

1970 • 242 citations

Grandes deviations et applications

1980 • 237 citations

Dynamic Programming Conditions for Partially Observable Stochastic Systems

1973 • 232 citations

Excursions in Brownian motion

1976 • 226 citations

Une solution simple au probleme de Skorokhod

1979 • 223 citations

On discontinuous additive functionals and Lévy measures of a Markov process

1964 • 220 citations

Poisson Point Processes Attached to Markov Processes

1987 • 213 citations

Generalized second order differential operators and their lateral conditions

1957 • 212 citations

Liens entre équations différentielles stochastiques et ordinaires

1977 • 210 citations

Semimartingales and Markov processes

1980 • 208 citations

Stochastic Differential Equations in a Differentiable Manifold

1950 • 206 citations

Stationary random distributions

1954 • 201 citations

Quelques applications de la formule de changement de variables pour les semimartingales

1970 • 201 citations

The Design of Robust Approximations to the Stochastic Differential Equations of Nonlinear Filtering

1978 • 194 citations

Fluctuation theory in continuous time

1975 • 192 citations

Bessel diffusions as a one-parameter family of diffusion processes

1973 • 192 citations

Derivatives of Wiener functionals and absolute continuity of induced measures

1980 • 186 citations

ON CONTINUOUS MARTINGALES

1965 • 183 citations

On Boundaries and Lateral Conditions for the Kolmogorov Differential Equations

1957 • 182 citations

Some Probabilistic Properties of Bessel Functions

1978 • 170 citations

On the infinite divisibility of the lognormal distribution

1977 • 168 citations

Kolmogoroff's theory of locally isotropic turbulence

1947 • 162 citations

Brownian Motion with a Several-Dimensional Time

1963 • 161 citations

Sojourn times of diffusion processes

1963 • 159 citations

Hitting probabilities of single points for processes with stationary independent increments

1969 • 159 citations

On a stochastic integral equation

1946 • 158 citations

A Stopped Brownian Motion Formula

1975 • 157 citations

Local times and sample function properties of stationary Gaussian processes

1969 • 156 citations

Processus de Markov

1967 • 152 citations

Embeddings and immersions in Riemannian geometry

1970 • 147 citations

On a multiplicative functional transformation arising in nonlinear filtering theory

1980 • 142 citations

Fluctuation identities for lévy processes and splitting at the maximum

1980 • 136 citations

On the pathwise uniqueness of solutions of one-dimensional stochastic differential equations

1972 • 134 citations

Demonstration simplifiee d'un theoreme de Knight

2006 • 123 citations

On Distributions of Functionals Related to Boundary Problems for Processes with Independent Increments

1966 • 120 citations

Markov processes and martin boundaries part I

1965 • 118 citations

Excursions of Brownian motion and bessel processes

1979 • 118 citations

Gaussian Processes with Stationary Increments: Local Times and Sample Function Properties

1970 • 117 citations

Decomposing the Brownian path

1970 • 115 citations

On the Existence, Uniqueness, Convergence and Explosions of Solutions of Systems of Stochastic Integral Equations

1977 • 113 citations

�tude des solutions extr�males et repr�sentation int�grale des solutions pour certains probl�mes de martingales

1977 • 109 citations

On a comparison theorem for solutions of stochastic differential equations and its applications

1973 • 108 citations

The student t-distribution of any degree of freedom is infinitely divisible

1976 • 108 citations

Grossissement d’une filtration et semi-martingales : Formules explicites

1978 • 106 citations

Study of a filtration expanded to include an honest time

1978 • 104 citations

Excursions of a Markov Process

1979 • 103 citations

Markov processes and Martin boundaries

1963 • 102 citations

Formules de la moyenne, calcul de perturbations et théorèmes d'annulation pour les formes harmoniques

1974 • 99 citations

Syst�mes de l�vy des processus de markov

1973 • 97 citations

Necessary and Sufficient Conditions for Almost Sure Sample Stability of Linear Ito Equations

1971 • 92 citations

Resolvents, Transition Functions, and Strongly Markovian Processes

1959 • 91 citations

Proof of the law of iterated logarithm through diffusion equation

1959 • 83 citations

Boundaries induced by non-negative matrices

1956 • 81 citations

Theory of Markov Processes.

1962 • 78 citations

Local times for Markov processes

1964 • 77 citations

To reverse a Markov process

1969 • 76 citations

Une Generalisation des Processus à Accroissements Positifs Independants

1961 • 74 citations

On Decomposition Theorems of Meyer.

1969 • 74 citations

Resultats de Kesten sur les processus a accroissements independants

2006 • 73 citations

Probabilistic approach in potential theory to the equilibrium problem

1973 • 70 citations

A Path Decomposition for Markov Processes

1978 • 70 citations

Last Exit Times and Additive Functionals

1973 • 69 citations

On the integral representation of functionals of ltd processest

1980 • 68 citations

The Martin boundary for Polya's urn scheme, and an application to stochastic population growth

1964 • 66 citations

On a class of additive functionals of Markov processes

1965 • 65 citations

Harmonic analysis of local times and sample functions of Gaussian processes

1969 • 64 citations

Classical mechanics, the diffusion (heat) equation and the Schrödinger equation on a Riemannian manifold

1981 • 63 citations

Class 𝐷 supermartingales

1963 • 63 citations

Systèmes markoviens et stationnaires. Cas dénombrable

1951 • 62 citations

Presentation Unifiee de Certaines Inegalites de la Theorie des Martingales

2002 • 62 citations

Markov properties of Brownian local time

1969 • 59 citations

Brownian local times

1975 • 58 citations

Last Exit Decompositions and Distributions

1973 • 57 citations

On Brownian motion in a homogeneous Riemannian space

1952 • 56 citations

Dual Markov processes: Construction of a useful auxiliary process

1979 • 55 citations

Hölder conditions for realizations of Gaussian processes

1961 • 55 citations

Denumerable Markov Processes (II)

1959 • 54 citations

Finely holomorphic functions

1980 • 54 citations

Limit Theorems for Markov Processes

1958 • 54 citations

Excursions of a non-singular diffusion

1963 • 54 citations

Approximating Countable Markov Chains

1983 • 53 citations

A reduction of continuous square-integrable martingales to Brownian motion

1971 • 52 citations

Picard’s theorem and Brownian motion

1975 • 50 citations

Existence du processus croissant naturel associ� � un potentiel de la classe (D)

1968 • 49 citations

Construction of Local Time and Poisson Point Processes from Nested Arrays

1980 • 49 citations

The Bessel Polynomials and the StudenttDistribution

1976 • 47 citations

Stochastic Riemannian Geometry

1978 • 47 citations

Stochastic parallel displacement

1975 • 47 citations

Equations differentielles stochastiques

1977 • 46 citations

Note on regularization of markov processes

1965 • 46 citations

Coterminal families and the strong Markov property

1973 • 44 citations

The Infinite Divisibility of the Von Mises-Fisher Distribution for All Values of the Parameter in all Dimensions

1977 • 41 citations

Séminaire de Probabilités XII

1978 • 40 citations

Splitting times and shift functionals

1979 • 39 citations

L�vy's downcrossing theorem

1977 • 38 citations

Conditional Distributions and Tightness

1974 • 37 citations

Multiple points for symmetric Lévy processes

1978 • 36 citations

Splitting times for Markov processes and a generalised Markov property for diffusions

1974 • 36 citations

The Condenser Problem

1977 • 33 citations

A note on the Q-matrices of Markov Chains

1967 • 31 citations

Meyer's theorem on predictability

1974 • 30 citations

A TOTALLY UNSTABLE DENUMERABLE MARKOV PROCESS

1958 • 26 citations

An Introduction to Stochastic Differential Equations on Manifolds

1973 • 26 citations

On a stopped Brownian motion formula of H.M. Taylor

1976 • 25 citations

The $Q$-matrix problem for Markov chains

1975 • 25 citations

SOME THEOREMS CONCERNING RESOLVENTS OVER LOCALLY COMPACT SPACES

1967 • 25 citations

Lattice Methods and Submarkovian Processes

1961 • 23 citations

The Measure of the Range of a Subordinator

1973 • 22 citations

Ensembles aléatoires markoviens homogènes (III)

2006 • 21 citations

Dual markov functionals: Applications of a useful auxiliary process

1979 • 21 citations

State spaces for Markov chains

1970 • 21 citations

The Knotting of Brownian Motion in 3-Space

1979 • 19 citations

Sur les états d'entrée et les états fictifs d'un processus de Markov

1962 • 17 citations

Excision of a strong Markov process

1972 • 17 citations

Brownian Motions and Diffusions as Markov Processes

1974 • 15 citations

Conditional excursion theory

1979 • 15 citations

Application of additive functionals to the boundary problem of Markov processes. Lévy's system of U-processes

1967 • 14 citations

The Q-matrix problem

1976 • 13 citations

Unbounded local times

1974 • 13 citations

The law of the iterated logarithm for Banach space valued random variables

1976 • 11 citations

Une Theorie de la Dualite a Ensemble Polaire Pres II

1976 • 10 citations

Processus markoviens et stationnaires. Cas dénombrable

1958 • 8 citations

Quelques exemples familiers, en probabilites, d’ensembles analytiques, non boreliens

1978 • 6 citations

Diffusions à coefficients continus d’après D.W. Stroock et S.R.S. Varadhan

1970 • 6 citations

Classical Potential Theory and Brownian Motion

1972 • 5 citations

Logarithmic Potentials and Planar Brownian Motion

1972 • 2 citations

Annonçabilite des temps previsibles: Deux contre-exemples

1980 • 2 citations

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