Ergodic control of diffusion processes

International Congress of Mathematicians, ICM 2006

Volumn 3, Issue , 2006, Pages 1299-1309

  Borkar, Vivek S ^a  

^a TATA INSTITUTE OF FUNDAMENTAL RESEARCH   (India)

Author keywords

Controlled diffusions; Controlled martingale problems; Dynamic programming; Ergodic control; Stationary Markov control

Indexed keywords

CONTROLLED DIFFUSION; DEGENERATE DIFFUSIONS; DIFFUSION PROCESS; ERGODIC CONTROL; INFINITE DIMENSIONAL; MARTINGALE PROBLEM; NONDEGENERATE; OPTIMAL CONTROLS;

DIFFUSION; DYNAMIC PROGRAMMING;

PROCESS CONTROL;

EID: 79952398726     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (35)

1. Allinger, D. F., Mitter, S. K., New results on the innovations problem of nonlinear filtering. Stochastics 4 (1981), 339-348.
2. Arapostathis, A., Borkar, V. S., Ghosh, M. K., Ergodic Control of Diffusion Processes. Book in preparation.
3. Arisawa, M., Ergodic problem for the Hamilton-Jacobi-Bellman equation I. Existence of the ergodic attractor. Ann. Inst. H. Poincaré Anal. Non Ĺaire 14 (1997), 415-438.
4. Arisawa, M., Ergodic problem for the Hamilton-Jacobi-Bellman equation II. Ann. Inst. H. Poincaré Anal. Non Linéaire 15 (1998), 1-24.
5. Basak, G., Borkar, V. S., Ghosh, M. K., Ergodic control of degenerate diffusions. Stochastic Anal. Appl. 15 (1997), 1-17.
6. Bensoussan, A., Frehse, J., On Bellman equations of ergodic control in Rn. J. Reine Angew. Math. 429 (1992), 125-160.
7. Bhatt, A. G., Borkar, V. S., Occupation measures for controlled Markov processes: characterization and optimality. Ann. Probab. 24 (1996), 1531-1562.
8. Bhatt, A. G., Borkar, V. S., Existence of optimal Markov solutions for ergodic control of Markov processes. Sankhya 67 (2005), 1-18.
9. Borkar, V. S., Optimal Control of Diffusion Processes. Pitman Research Notes in Math. 203, Longman Scientific and Technical, Harlow, UK, 1989.
10. Borkar, V. S., On extremal solutions to stochastic control problems. Appl. Math. Optim. 24 (1991), 317-330.
11. Borkar, V. S., Controlled diffusions with constraints II. J. Math. Anal. Appl. 176 (1993), 310-321.
12. Borkar, V. S., Dynamic programmimg for ergodic control with partial observations. Stochastic Process. Appl. 103 (2003), 293-310.
13. Borkar, V. S., Budhiraja, A., A further remark on dynamic programming for partially observed Markov processes. Stochastic Process. Appl. 112 (2004), 79-93.
14. Borkar, V. S., Budhiraja, A., Ergodic control for constrained diffusions: characterization using HJB equations. SIAM J. Control Optim. 43 (2004), 1463-1492.
15. Borkar, V. S., Gaitsgory, V., Singular perturbations in ergodic control of diffusions. Submitted.
16. Borkar, V. S., Ghosh, M. K., Ergodic control of multidimensional diffusions I: the existence results. SIAM J. Control Optim. 26 (1988), 112-126.
17. Borkar, V. S., Ghosh, M. K., Ergodic control of multidimensional diffusions II: adaptive control. Appl. Math. Optim. 21 (1990), 191-220.
18. Borkar, V. S., Ghosh, M. K., Controlled diffusions with constraints. J. Math. Anal. Appl. 152 (1990), 88-108.
19. Borkar, V. S., Ghosh, M. K., Stochastic differential games: an occupation measure based approach. J. Optim. Theory Appl. 73 (1992), 359-385; erratum ibid. 88, 251-252.
20. Borkar, V. S., Kumar, S., On extremal solutions of controlled non-linear filtering equations. SIAM J. Control Optim. 33 (1995), 718-724.
21. Borkar, V. S., Mitter, S. K., A note on stochastic dissipativeness. In Directions in Mathematical Systems Theory and Optimization (ed. by A. Rantzer and C. I. Byrnes), Lecture Notes in Control and Inform. Sci. 286, Springer-Verlag, Berlin, Heidelberg 2003, 41-49.
22. Fleming, W. H., McEneaney, W. M., Risk-sensitive control on an infinite horizon. SIAM J. Control Optim. 33 (1995), 1881-1915.
23. Ghosh, M. K., Arapostathis, A., and Marcus, S. I., Optimal control of switching diffusions with applications to flexible manufacturing systems. SIAM J. Control Optim. 31 (1993), 1183-1204.
24. Haussmann, U. G., L'Equation de Zakai et le Problème Séparé du Contrôle Optimal Stochastique. In Seminaire de Probabilites XIX (ed. by J. Azéma and M. Yor), Lecture Notes in Math. 1123, Springer-Verlag, Berlin, Heidelberg 1985, 37-62.
25. Helmes, K., Stockbridge, R. H., Numerical comparison of controls and verification of optimality for stochastic control problems. J. Optim. Theory Appl. 106 (2000), 107-127.
26. Krylov, N. V., Controlled Diffusion Processes. Applications of Mathematics 14, Springer- Verlag, New York, Heidelberg, Berlin 1980.
27. Kurtz, T. G., Stockbridge, R., Existence of Markov controls and characterization of Markov controls. SIAM J. Control Optim. 36 (1998), 609-653; erratum ibid. 37 (1999), 1310-1311.
28. Kushner, H. J., Dupuis, P., Numerical Methods for Stochastic Control Problems in Continuous Time. 2nd edition, Appl. Math. (N.Y.) 24, Springer-Verlag, New York 2001.
29. Menaldi, J.-L., Robin, M., Ergodic control of reflected diffusions with jumps. Appl. Math. Optim. 35 (1997), 117-137.
30. Menaldi, J.-L., Perthame, B., Robin, M., Ergodic problem for optimal stochastic switching. J. Math. Anal. Appl. 147 (1990), 512-530.
31. Menaldi, J.-L., Robin, M., Taksar, M. I., Singular ergodic control for multidimensional Gaussian processes. Math. Control Signals Systems 5 (1992), 93-114.
32. Robin, M., On some impulse control problems with long run average cost. SIAM J. Control Optim. 19 (1981), 333-358.
33. Stockbridge, R. H., Time-average control of martingale problems: existence of a stationary solution. Ann. Probab. 18 (1990), 190-205.
34. Stockbridge, R. H., Time-average control of martingale problems: a linear programming formulation. Ann. Probab. 18 (1990), 206-217.
35. Stroock, D. W., Varadhan, S. R. S., Multidimensional Diffusion Processes. Grundlehren Math.Wiss. 233, Springer-Verlag, Berlin, New York 1979.