Professor Thomas G. Kurtz


Ph.D., 1967, Stanford University
Professor Emeritus of Mathematics and Statistics

FAX:  (608) 263-8891

Mailing address:

Department of Mathematics
University of Wisconsin - Madison
480 Lincoln Drive
Madison, WI 53706-1388

Department of Statistics
University of Wisconsin - Madison
1300 University Avenue
Madison, WI 53706

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Research Interests

Recent research interests include stochastic partial differential equations, filtering for Markov processes, large deviations, stochastic control, limit theorems for stochastic differential equations, particle representations of measure-valued processes, and modeling of spatial point processes. Application areas include reaction networks, communication networks, genetics, and finance. 

Notes and Transparencies from Lectures

Recent Publications

The research reported in these publications was supported in part by the National Science Foundation. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.  Individuals without web access to any of these publications should e-mail

Large deviations for stochastic processes (with Jin Feng).   Mathematical Surveys and Monographs, 131. American Mathematical Society, Providence, RI, 2006.  Errata


Genealogical constructions of population models

(with Alison Etheridge)  Ann. Probab. (to appear)


Non-explosivity of stochastically modeled reaction networks that are complex balanced

(with David Anderson, Daniele Cappelletti, and Masanori Koyama) Bulletin Math. Bio. (to appear)


Existence and uniqueness of reflecting diffusions in cusps

(with Cristina Costantini) Electron. J. Probab.  (to appear)


Particle representations for stochastic partial differential equations with boundary conditions  

(with Dan Crisan and Christopher Janjigian) Electron J. Probab. 23  (2018) no. 65, 1-29.


Finite time distributions of stochastically modeled chemical systems with absolute concentration robustness

(with David Anderson and Daniele Cappalletti) SIAM J. Applied Dynamical Systems 16 (2017) 1309-1339.


Tightness for processes with fixed points of discontinuities and applications in varying environment  

(with Vincent Bansaye and Florian Simatos) Electron. Commun. Probab. 21 (2016) no.81, 1-9.


Viscosity methods giving uniqueness for martingale problems

(with Cristina Costantini) Electron. J. Probab. 20 (2015) no. 67, 1-27.


Weak and strong solutions of general stochastic models

Electron. Commun. Probab. 19 (2014), no. 58, 1-16.


Central limit theorems and diffusion approximations for multiscale Markov chain models

(with Hye-Won Kang and Lea Popovic) Ann. Appl. Probab. 24 (2014), 721-759.



A CLT for empirical processes involving time dependent data

(with James Kuelbs and Joel Zinn)  Ann. Probab. 41 (2013), 785-816.



Conditional distributions, exchangeable particle systems, and stochastic partial differential equations

(with Dan Crisan and Yoonjung Lee)  Annales de l’Institut Henri Poincaré   (to appear)



Separation of time-scales and model reduction for stochastic reaction models

(with Hye-Won Kang)  Ann. Appl. Probab. 23 (2013), 529-583.



Continuous-time Markov chain models for chemical reaction networks

(with David Anderson) Design and Analysis of Biomolecular Circuits, H. Koeppl, D. Densmore, G. Setti, M. di Bernardo eds. (2011), 3-42.



Equivalence of stochastic equations and martingale problems.

Stochastic Analysis 2010. Dan Crisan, Ed.  (2011), 113-130.



Error analysis of tau-leap simulation methods. 

(with David Anderson and Arnab Ganguly) Ann. Appl. Probab. 21 (2011), 226-2262.



The filtered martingale problem. 

(with Giovanna Nappo)  The Oxford Handbook of Nonlinear Filtering, Dan Crisan and Boris Rozovskii, eds.  (2011), 129-165.



Macroscopic limits for stochastic partial differential equations of McKean-Vlasov type

(with Peter Kotolenez) Probab. Theory Relat. Fields 146 (2010), 189-222.



Limit theorems for an epidemic model on the complete graph

(with E. Lebensztayn, A. R. Leichsenring, and F. P. Machado). ALEA Lat. Am. J. Probab. Math. Stat. 4 (2008), 45--55.


Poisson representations of branching Markov and measure-valued branching processes

(with Eliane Rodrigues).  Ann. Probab. 39 (2011), 939-984.



Spatial point processes and the projection method

(with Nancy Lopes Garcia) In and Out of Equilibrium 2, V. Sidoravicius and M. E. Vares, eds.  Progress in Probability 60 (2008), 271-298.



The Yamada-Watanabe-Engelbert theorem for general stochastic equations and inequalities

Elec. J. Probab. 12, (2007), 951-965.


Spatial birth and death processes as solutions of stochastic equations

(with Nancy Lopes Garcia) ALEA Lat. Am. J. Probab. Math. Stat. 1, (2006), 281-303.


Asymptotic analysis of multiscale approximations to reaction networks

(with Karen Ball, Lea Popovic, and Greg Rempala) Ann. Appl. Probab. 16 (2006), 1925-1961.



Diffusion approximations of transport processes with general reflecting boundary conditions

(with Cristina Costantini) Math. Models Methods Appl. Sci. 16 (2006), 717-762.


A stochastic evolution equation arising from the fluctuation of a class of interacting particle systems

(with Jie Xiong) Comm. Math. Sci. 2 (2004), 325-358.


The approximate Euler method for Lévy driven stochastic differential equations

(with Jean Jacod, Sylvie Méléard, and Philip Protter) Ann. Inst. H. Poincaré Probab. Statist. 41 (2005), 523-558.


Time-invariance modeling and estimation for spatial point processes:  General theory

(with Shun-Hwa Li)

dvi postscript pdf


When can one detect overdominant selection in the infinite alleles model?

(with Paul Joyce and Stephen M. Krone). Ann. Appl. Probab. 13 (2003), 181-212.



 Stationary solutions and forward equations for controlled and singular martingale problems

(with Richard H. Stockbridge) Elec. J. Probab. 6 (2001), paper 15.


 Gaussian limits associated with the Poisson-Dirichlet distribution and the Ewens sampling formula

(with Paul Joyce and Stephen M. Krone). Ann. Appl. Probab. 12 (2002), 101-124.



Mixed time scale recursive algorithms

(with James A. Bucklew). IEEE Transactions on Signal Processing 49 (2001), 1824 - 1830.



Numerical solutions for a class of SPDEs with application to filtering

(with Jie Xiong). Stochastics in Finite/Infinite Dimensions (in honor of Gopinath Kallianpur). (2001), 233-258. Birkhäuser, Boston.



Martingale problems and linear programs for singular control

(with Richard H. Stockbridge). 37th annual Allerton Conference on Communication Control and Computing (Monticello, Ill. 1999), 11-20, Univ. Illinois, Urbana-Champaign, Ill.



Particle representations for measure-valued population processes with spatially varying birth and death rates.

Proceedings of International Conference on Stochastic Models (Ottawa, June, 1998) ). CMS Conference Proceedings, 26, 299-317. AMS, Providence.



Genealogical processes for Fleming-Viot models with selection and recombination

(with Peter Donnelly). Ann. Appl. Probab. 9 (1999), 1091-1148.



Continuum-sites stepping-stone models, coalescing exchangeable partitions, and random trees

(with Peter Donnelly, Steven N. Evans, Klaus Fleischmann, and Xiaowen Zhou). Ann. Probab. 28 (2000), 1063-1110.



Particle representations for a class of nonlinear SPDEs

(with Jie Xiong) Stochastic Process Appl. 83 (1999), 103-126.


Particle representations for measure-valued population models

(with Peter Donnelly). Ann. Probab. 27 (1999), 166-205.



Existence of Markov controls and characterization of optimal Markov controls

(with Richard Stockbridge). SIAM J. Control Optim. 36 (1998), 609-653.

Erratum SIAM J. Control Optim. 37 (1999), 1310-1311


Martingale problems for conditional distributions of Markov processes.

Elec. J. Probab. 3 (1998), paper 9.


Coupling and ergodic theorems for Fleming-Viot processes

(with Stewart Ethier). Ann. Probab. 26 (1998), 533-561.



The changing nature of network traffic: Scaling phenomena

(with A. Feldman, A. C. Gilbert and W. Willinger). ACM SIGCOMM Computer Communication Review, April, 1998.





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