Thomas G. Kurtz | Academic Influence

Thomas G. Kurtz's AcademicInfluence.com Rankings

Thomas G. Kurtz

Mathematics

#2587

World Rank

#3969

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Measure Theory

#808

World Rank

#1071

Historical Rank

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Mathematics

Thomas G. Kurtz's Degrees

PhD Mathematics Princeton University
Bachelors Mathematics Dartmouth College

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Why Is Thomas G. Kurtz Influential?

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According to Wikipedia, Thomas G. Kurtz is an American emeritus professor of Mathematics and Statistics at University of Wisconsin-Madison known for his research contributions to many areas of probability theory and stochastic processes. In particular, Kurtz’s research focuses on convergence, approximation and representation of several important classes of Markov processes. His findings appear in scientific disciplines such as systems biology, population genetics, telecommunications networks and mathematical finance.

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Thomas G. Kurtz'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

Markov Processes: Characterization and Convergence (2005) (4403)
Stochastic equations in infinite dimensions (2006) (2758)
Solutions of ordinary differential equations as limits of pure jump markov processes (1970) (960)
Approximation of Population Processes (1987) (594)
Limit theorems for sequences of jump Markov processes approximating ordinary differential processes (1971) (562)
Weak Limit Theorems for Stochastic Integrals and Stochastic Differential Equations (1991) (555)
Strong approximation theorems for density dependent Markov chains (1978) (542)
The Relationship between Stochastic and Deterministic Models for Chemical Reactions (1972) (541)
Large Deviations for Stochastic Processes (2006) (441)
The changing nature of network traffic: scaling phenomena (1998) (368)
Continuous Time Markov Chain Models for Chemical Reaction Networks (2011) (285)
Particle Representations for Measure-Valued Population Models (1999) (274)
A limit theorem for perturbed operator semigroups with applications to random evolutions (1973) (256)
Product-Form Stationary Distributions for Deficiency Zero Chemical Reaction Networks (2008) (229)
ASYMPTOTIC ANALYSIS OF MULTISCALE APPROXIMATIONS TO REACTION NETWORKS (2005) (222)
Fleming-Viot processes in population genetics (1993) (206)
Stochastic Analysis of Biochemical Systems (2015) (197)
Particle representations for a class of nonlinear SPDEs (1999) (185)
A countable representation of the Fleming-Viot measure-valued diffusion (1996) (175)
Existence of Markov Controls and Characterization of Optimal Markov Controls (1998) (165)
Semigroups of Conditioned Shifts and Approximation of Markov Processes (1975) (165)
Separation of time-scales and model reduction for stochastic reaction networks. (2010) (161)
Extensions of Trotter's operator semigroup approximation theorems (1969) (153)
Averaging for martingale problems and stochastic approximation (1992) (146)
Genealogical processes for Fleming-Viot models with selection and recombination (1999) (140)
Unique characterization of conditional distributions in nonlinear filtering (1984) (125)
Convergence of sequences of semigroups of nonlinear operators with an application to gas kinetics (1973) (122)
Limit theorems and diffusion approximations for density dependent Markov chains (1976) (119)
Equivalence of Stochastic Equations and Martingale Problems (2011) (117)
A Conceptual Proof of the Kesten-Stigum Theorem for Multi-Type Branching Processes (1997) (115)
The infinitely-many-neutral-alleles diffusion model (1981) (112)
Weak convergence of stochastic integrals and differential equations (1996) (109)
The Yamada-Watanabe-Engelbert theorem for general stochastic equations and inequalities (2007) (108)
Large loss networks (1994) (108)
Error analysis of tau-leap simulation methods (2009) (107)
Wong-Zakai Corrections, Random Evolutions, and Simulation Schemes for SDE's (1991) (102)
Stratonovich stochastic differential equations driven by general semimartingales (1995) (101)
Martingale Problems for Conditional Distributions of Markov Processes (1998) (99)
Representations of Markov Processes as Multiparameter Time Changes (1980) (95)
Weak convergence and local stability properties of fixed step size recursive algorithms (1993) (94)
The approximate Euler method for Lévy driven stochastic differential equations (2005) (94)
Probabilistic Models for Nonlinear Partial Differential Equations (1996) (88)
Random Time Changes and Convergence in Distribution Under the Meyer-Zheng Conditions (1991) (87)
Weak convergence of stochastic integrals and differential equations II: Infinite dimensional case (1996) (79)
Spatial birth and death processes as solutions of stochastic equations (2006) (75)
Limit theorems for workload input models (2000) (73)
Macroscopic limits for stochastic partial differential equations of McKean–Vlasov type (2008) (71)
Convergence to Fleming-Viot processes in the weak atomic topology (1994) (70)
Berry-Esseen Estimates in Hilbert Space and an Application to the Law of the Iterated Logarithm (1974) (69)
Weak and strong solutions of general stochastic models (2013) (67)
The infinitely-many-alleles model with selection as a measure-valued diffusion (1987) (63)
Stationary Solutions and Forward Equations for Controlled and Singular Martingale Problems (2001) (62)
Central limit theorems and diffusion approximations for multiscale Markov chain models (2012) (59)
A stochastic evolution equation arising from the fluctuations of a class of interacting particle systems (2004) (50)
The Optional Sampling Theorem for Martingales Indexed by Directed Sets (1980) (48)
A general theorem on the convergence of operator semigroups (1970) (40)
Numerical Solutions for a Class of SPDEs with Application to Filtering (2001) (39)
Representation and approximation of counting processes (1982) (38)
A multiclass Station with Markovian Feedback in Heavy Traffic (1995) (35)
A random Trotter product formula (1972) (35)
CONTINUUM-SITES STEPPING-STONE MODELS, COALESCING EXCHANGEABLE PARTITIONS AND RANDOM TREES (1998) (35)
Particle Representations for Measure-Valued Population Processes With Spatially Varying Birth Rates (1998) (35)
Finite Time Distributions of Stochastically Modeled Chemical Systems with Absolute Concentration Robustness (2016) (32)
Non-explosivity of Stochastically Modeled Reaction Networks that are Complex Balanced (2017) (31)
Applications of duality to measure-valued diffusion processes (1982) (30)
Limit theorems for an epidemic model on the com- plete graph (2008) (30)
Necessary and Sufficient Conditions for Complete Convergence in the Law of Large Numbers (1980) (28)
When can one detect overdominant selection in the infinite-alleles model? (2003) (27)
GAUSSIAN LIMITS ASSOCIATED WITH THE POISSON-DIRICHLET DISTRIBUTION AND THE EWENS SAMPLING FORMULA (2002) (26)
Landau-Kolmogorov inequalities for semigroups and groups (1977) (25)
Martingale problems for controlled processes (1987) (23)
Coupling and ergodic theorems for Fleming-Viot processes (1998) (23)
Spatial Point Processes and the Projection Method (2008) (23)
Inequalities for the Law of Large Numbers (1972) (22)
The filtered martingale problem (2009) (21)
Viscosity methods giving uniqueness for martingale problems (2014) (21)
Conditional distributions, exchangeable particle systems, and stochastic partial differential equations (2014) (20)
Poisson representations of branching Markov and measure-valued branching processes. (2011) (19)
Relationships between stochastic and deterministic population models (1980) (19)
Generators and Markov Processes (2008) (19)
On the Stationary Distribution of the Neutral Diffusion Model in Population Genetics (1992) (18)
Martingale Problems for Constrained Markov Problems (1990) (18)
Generalization of Dynkin's Identity and Some Applications (1973) (18)
Genealogical constructions of population models (2014) (18)
Stochastic Analysis: Characterizing the weak convergence of stochastic integrals (1991) (17)
On the Functional Central Limit Theorem for the Ewens Sampling Formula (1991) (16)
A CLT for empirical processes involving time-dependent data (2010) (15)
The Central Limit Theorem for Markov Chains (1981) (15)
The asymptotic behavior of an urn model arising in population genetics (1996) (14)
An abstract averaging theorem (1976) (14)
Point processes and completely monotone set functions (1974) (13)
Approximation of Discontinuous Processes by Continuous Processes (1981) (12)
DIFFUSION APPROXIMATION FOR TRANSPORT PROCESSES WITH GENERAL REFLECTION BOUNDARY CONDITIONS (2006) (12)
Martingale problems and linear programs for singular control ∗ (1999) (10)
A Counterexample for the Trotter Product Formula. (1984) (10)
Comparison of Semi-Markov and Markov Processes (1971) (8)
Correlation and variability in birth processes (1993) (7)
Existence and uniqueness of reflecting diffusions in cusps (2017) (7)
A martingale problem for conditional distributions and uniqueness for the nonlinear filtering equations (1985) (7)
Linear Programming Formulations of Singular Stochastic Control Problems: Time-Homogeneous Problems (2017) (7)
A Probabilistic Distributed Algorithm for Set Intersection and its Analysis (1987) (7)
Tightness for processes with fixed points of discontinuities and applications in varying environment (2014) (5)
Particle representations for stochastic partial differential equations with boundary conditions (2016) (5)
Markov selection for constrained martingale problems (2019) (5)
Particle representations for measure-valued population models 1 June 1 , 1998 (1998) (4)
Wiley Series in Probability and Statistics (1986) (4)
Erratum to: Models of biochemical reaction systems (2015) (4)
Finite Markov chains coupled to general Markov processes and an application to metastability. (2019) (4)
A Note on Sequences of Continuous Parameter Markov Chains (1969) (4)
The Nonexistence of the Yaglom Limit for An Age Dependent Subcritical Branching Process (1973) (3)
On numerical calculation of transonic flow patterns (1968) (2)
Approximation of Age Dependent, Multitype Branching Processes (1970) (2)
An inhomogeneous reverse ergodic theorem and application to a new uniqueness result for reflecting diffusions. (2021) (2)
Stochastic Processes and Their Applications the Conference Organizing Committee the Scientific Committee Bálint Tóth (budapest) Feng-yu Wang (beijing) Ii in Memoriam (2007) (2)
A Variational Formula for the Growth Rate of a Positive Operator Semigroup (1979) (2)
Stochastic Processes and Martingales (2008) (2)
A Probabilistic Distributed Algorithm for Set Intersection and Its Analysis (Preliminary Version) (1985) (1)
Ergodicity and Central Limit Theorems for Markov Processes (2016) (1)
Particle representation for the solution of the filtering problem. Application to the error expansion of filtering discretizations (2021) (1)
Analytic approaches to model simplification and approximation (2015) (1)
Invariance Principles and Diffusion Approximations (2008) (1)
Reaction Networks and Population Dynamics (2018) (1)
Erratum: "Existence of Markov Controls and Characterization of Optimal Markov Controls" (1999) (1)
Approaches to weak convergence (1984) (1)
Localization for constrained martingale problems and optimal conditions for uniqueness of reﬂecting diﬀusions in 2-dimensional piecewise smooth domains (2022) (1)
Models of biochemical reaction systems (2015) (1)
Mixed time scale recursive algorithms (2001) (1)
Hénard, Olivier Change of measure in the lookdown (2021) (0)
Linear programming formulations of stochastic control problems (1998) (0)
The purpose of the Institute is to foster the development and dissemination of the theory and applications of statistics and probability. (2016) (0)
Localization for constrained martingale problems and optimal conditions for uniqueness of reflecting diffusions in 2-dimensional domains (2022) (0)
Examples of Generators (2008) (0)
A NOTE ON SEQUENCES OF CONTINUOUS PARAMETER (2016) (0)
Bibliography [1] Linda Allen, Stochastic Processes with Applications to Biology, Pearson, New (2011) (0)
Multiscale methods in a Heat Shock Response Model (2007) (0)
3. Markov Processes and Their Generators (1981) (0)
Genealogical constructions and asymptotics for continuous-time Markov and continuous-state branching processes (2018) (0)
Stationary distributions of stochastically modeled reaction systems (2015) (0)
Extensions of viscosity solution methods (2006) (0)
Results from mass transport theory (2006) (0)
The comparison principle (2006) (0)
Density Dependent Population Processes (2008) (0)
Acknowledgment of Priority: The Central Limit Theorem for Markov Chains (1984) (0)
10. Random Replication with Errors (1981) (0)
Large deviations for Markov processes and nonlinear semigroup convergence (2006) (0)
The Nisio semigroup and a control representation of the rate function (2006) (0)
Branching Processes: Large Populations (2005) (0)
Infinitesimal specification of continuous time Markov chains (2015) (0)
A reverse ergodic theorem for inhomogeneous killed Markov chains and application to a new uniqueness result for reflecting diffusions (2021) (0)
Erratum to "Convergence of Sequences of Semigroups of Nonlinear Operators With an Application to Gas Kinetics" (1975) (0)
Erratum to: “Convergence of sequences of semigroups of nonlinear operators with an application to gas kinetics” (Trans. Amer. Math. Soc. 186 (1973), 259–272, 1974) (1975) (0)
Variational constants, rate of growth and spectral theory for the semigroup of positive linear operators (2006) (0)
Conference on Stochastic Processes and Their Applications (18) Held in Madison, Wisconsin on 25 June - 1 July 1989 (1989) (0)
Genealogies for stochastic population models (2019) (0)
Spectral properties for discrete and continuous Laplacians (2006) (0)
Non-explosivity of Stochastically Modeled Reaction Networks that are Complex Balanced (2018) (0)
Large deviations and nonlinear semigroup convergence using viscosity solutions (2006) (0)
Convergence of Probability Measures (2008) (0)
Random Time Changes (2008) (0)
4. Convergence to Markov Processes (1981) (0)
Stochastic Integral Equations (2008) (0)
9. Epidemic Models (1981) (0)
Applications of multiparameter stopping times (1978) (0)
Large deviations and exponential tightness (2006) (0)
Results on local stability of fixed step size recursive algorithms (1992) (0)
8. Approximations of Density Dependent Jump Markov Processes (1981) (0)
Control and Pricing in Communication and Power Networks 8-13 March 2004 (0)
7. Markov Processes as Random Time Changes (1981) (0)
2. Weak Convergence in DE [ 0,∞) (1981) (0)
Title : Mathematical Modeling of Cell Metabolism Name : (2011) (0)
MEYER-ZHENG CONDITIONS' (2016) (0)
Nearly deterministic processes in (2006) (0)
6. Branching Markov Processes (1981) (0)
Time-invarian e modeling and estimationfor spatial point pro esses : General theoryThomas (2003) (0)
Operators and convergence in function spaces (2006) (0)

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