FAX: (608) 263-8891
Department of Mathematics
University of Wisconsin - Madison
Department of Statistics
University of Wisconsin - Madison
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.
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 firstname.lastname@example.org.
(with Alison Etheridge)
Central limit theorems and diffusion approximations for multiscale Markov chain models
A CLT for empirical processes involving time dependent data
Conditional distributions, exchangeable particle systems, and stochastic partial differential equations
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.
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
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
The approximate Euler method for Lévy driven stochastic differential equations
(with Jean Jacod, Sylvie Méléard, and
Time-invariance modeling and estimation for spatial point processes: General theory
(with Shun-Hwa Li)
When can one detect overdominant selection in the infinite alleles model?
Stationary solutions and forward equations for controlled and singular martingale problems
Gaussian limits associated with the Poisson-Dirichlet distribution and the Ewens sampling formula
Mixed time scale recursive algorithms
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
Particle representations for a class of nonlinear SPDEs
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
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