Applied Mathematics

Wendell Fleming

Professor Emeritus of Applied Mathematics
Room 214, 170 Hope Street


Ph.D., 1951, University of Wisconsin


1. Functions of Several Variables, Addison-Wesley, 1965, 2nd ed., Springer-Verlag, 1977. 

2. Deterministic and Stochastic Optimal Control, (with R.W. Rishel), Springer-Verlag, 1975. 

3. Advances in Filtering and Optimal Stochastic Control, (co-editor with L.G. Gorostiza), Springer Lecture. Notes in Control and Information Sciences, No. 42 (1982). 

4. Recent Advances in Dynamic Programming, (co-editor with I. Capuzzo-Dolcetta and T. Zolezzi), Springer Lecture Notes in Math, No. 1119, 1985. 

5. Controlled Markov Processes and Nonlinear Evolution Equations, Accademia Nazionale dei Lincei, Scuola Normale Superiore, 1987. 

6. Stochastic Differential Systems, Stochastic Control Theory and Applications, (co-editor with P.L. Lions) IMA Volumes in Math. and its Applications No. 10, Springer-Verlag, 1987. 

7. Controlled Markov Processes and Viscosity Solutions, (with H. M. Soner) Springer-Verlag, 1992; Second Edition, 2006. 

Historical Articles

Early Developments in Geometric Measure Theory

De Giorgi and Geometric Measure Theory

Geometric Measure Theory at Brown in the 1960s

Remembrances of Life as a Young Husband and Mathematician

Remembrances of My Career at Brown University, 1958-1978



Faculty Research Profile


NSF Senior Postdoctoral Fellow 1968–69.

Guggenheim Fellow 1976–77.

Invited Plenary speaker, 1982 International Congress of
Mathematicians, in Warsaw. (Postponed until August 1983.)

Fermi Lecturer, Scuola Normale Superiore Pisa, 1986.

Steele Prize, American Mathematical Society, 1987.

Plenary Speaker IEEE Conference on Decision and Control 1988.

Doctor of Science, Honoris Causa, Purdue University, 1991.

Reid Prize, Society for Industrial and Applied Math., 1994.

American Academy of Arts and Sciences, 1995.

Isaacs Award, International Society for Dynamic Games, 2006.

Fellow, Society for Industrial and Applied Mathematics, 2009.

Election to the National Academy of Sciences, May 1, 2012


  1. Risk sensitive control on an infinite time horizon, (with W.M. McEneaney) SIAM Journal on Control and Optimiz., 33, (1995) 1881-1915.

  2. Optimal investment models and risk sensitive stochastic control, in IMA Volumes in Math and Applic., No. 65, (1995) 75-88.

  3. The risk-sensitive index and the H2 and H norms for nonlinear systems, (with M.R. James) Math. of Control, Signals and Sys, 8, (1995) 199-221.

  4. Risk sensitive control of finite state machines on an infinite horizon I, (with D. Hernandez-Hernandez) SIAM Journal on Control and Optimiz., 35, (1997) 1790-1810.

  5. Some results and problems in risk sensitive stochastic control, Computational and Applied Math., 16, (1997) 99-115.

  6. Asymptotics for the principal engenvalue and eigenvetor of a nearly first order operator with large potential, (with S.-J. Sheu) Annals of Probab., 25, (1997) 1953- 1994.

  7. Risk-sensitive production planning of a stochastic manufacturing system, (with Q. Zhang) SIAM Journal on Control and Optimiz., 36, (1998) 1147-1170.

  8. Risk sensitive control of finite state machines on an infinite horizon II, (with D. Hernandez-Hernandez), SIAM Journal on Control and Optimiz., 37 (1999) 1048-1069.

  9. Deterministic nonlinear filtering, Annali Scuola Normale Superiore Pisa, Sci. Fis. Matem. Se . 4, 25 (1997) 435-454.

  10. A max-plus based algorithm for an HJB equation of nonlinear filtering, (with W.M. McEneaney) SIAM Journal on Control and Optimiz., 38 (2000) 683-710.

  11. Optimal long term growth rate of expected utility of wealth, (with S.-J. Sheu) Ann. Appl. Prob. 9 (1998) 871-903.

  12. Risk sensitive control and an optimal investment model, (with S.-J. Sheu) Math. Finance, 10 (2000) 197-213.

  13. Stochastic optimal control, international finance and debt, (with J.L. Stein), J. of Banking and Finance, 28 (2004) 979-996.

  14. Controlled Markov processes and mathematical finance, in Nonlinear Analysis Differential Equations and Control, (ed. F.H. Clarke and R.J. Stein), Kluwer Academic Publishers, NATO Science Series C: Math. Phys. Sci., Vol. 528, (1999), 407-446.

  15. Deterministic and stochastic approaches to nonlinear filtering, (with W.M. McEneaney) Math. Control Signals Systems, 14 (2001) 109-142.

  16. Risk sensitive control and an optimal investment model II, (with S.-J. Sheu) Annals Appl. Probab., 12 (2002) 730-767. 

  17. Stochastic control models of optimal investment and consumption, Aportaciones Mathematicas, 16 (2001) 159-203.

  18. Max-plus stochastic processes, Applied Math. Optim., 49 (2004) 159-181. 

  19. An optimal consumption model with stochastic volatility (with D. Hernandez-Hernandez), Finance and Stochastics, 7 (2003) 245-262.

  20. An application of stochastic control theory to financial economics, (with T. Pang) SIAM J. Control Optimiz. 43(2004) 502-531.

  21. A stochastic control model of investment, production and consumption, (with T. Pang) Quarterly of Applied Math. 63 (2005) 71-85.

  22. The trade off between consumption and investment in incomplete financial markets (with D. Hernandez-Hernandez), Applied Math. Optim. 52 (2005) 219-234.

  23. Optimal investment models with minimum consumption criteria, Australian Economic Papers 44 (2005), 307-321.

  24. Risk sensitive stochastic control and differential games, Communications in Information and Systems, 6 (2006) 161-179. 

  25. Max-plus stochastic control and risk sensitivity (with H. Kaise and S. –J. Sheu), Applied Math. Optimiz 62 (2010) 81-144.

  26. On the value of stochastic differential games (with D. Hernandez-Hernandez),  Communications on Stochastic Analysis,  5  No. 2 (2011) 341-351. 

  27. Mixed Strategies for deterministic differential games (with D. Hernandez-Hernandez), Communications on Stochastic Analysis, 11 (2017) 137-156.