Ph.D., 1967,
Stanford University

Professor Emeritus of Mathematics and Statistics

FAX: (608) 263-8891

kurtz@math.wisc.edu

Mailing address:

Department of Mathematics

University of Wisconsin - Madison

480

Department of Statistics

University of Wisconsin - Madison

1300

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**Institute of Mathematical Statistics**

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Probability Society**

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**Institute for Mathematics
and its Applications **

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Biosciences Institute**

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**Mathematical Sciences Research Institute**

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**Statistical and Applied Mathematical
Sciences Institute**

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**Institute for Pure and Applied
Mathematics**

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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 kurtz@math.wisc.edu. **

*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.**

**(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.***
**

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**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 *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)

**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). *37 ^{th}
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.

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**Genealogical processes for
Fleming-Viot models with selection and recombination**

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

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**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.

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**Particle representations
for a class of nonlinear SPDEs**

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

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**Particle representations
for measure-valued population models**

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

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**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*

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**Martingale problems for
conditional distributions of Markov processes.**

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

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**Coupling and ergodic theorems for Fleming-Viot
processes**

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

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**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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