Stationary solutions and forward equations for controlled and singular martingale problems

Electronic Journal of Probability

Volumn 6, Issue , 2001, Pages 1-52

  Stockbridge, Richard H ^b  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

^b UNIVERSITY OF KENTUCKY   (United States)

Author keywords

Constrained Markov processes; Forward equations; Markov processes; Martingale problems; Singular controls; Stationary processes

Indexed keywords

EID: 1942498781     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v6-90     Document Type: Article

References (29)

1. A.G. Bhatt and V. S. Borkar, Occupation measures for controlled Markov processes: Characterization and optimality, Ann. Probab. 24 (1996), 1531-1562.
2. A.G. Bhatt and R.L. Karandikar, Invariant measures and evolution equations for Markov processes, Ann. Probab. 21 (1993), 2246-2268.
3. A.G. Bhatt, G. Kallianpur and R.L. Karandikar, Uniqueness and robustness of solutions of measurevalued equations of nonlinear filtering, Ann. Probab. 23 (1995), 1895-1938.
4. A.G. Bhatt, and R.L. Karandikar, Evolution equations for Markov processes: application to the white-noise theory of filtering, Appl. Math. Optim. 31 (1995), 327-348.
5. A.G. Bhatt and R.L. Karandikar, Characterization of the optimal filter: the non-Markov case, Stochastics Stochastics Rep., 66 (1999), 177-204.
6. V.S. Borkar and M.K. Ghosh, Ergodic control of multidimensional diffusions I: The existence results, SIAM J. Control Optim. 26 (1988), 112-126.
7. J. G. Dai and J. M. Harrison, Steady-State Analysis of RBM in a Rectangle: Numerical Methods and a Queueing Application, Ann. Appl. Probab. 1 (1991), 15-35.
8. M. H. A. Davis and A. R. Norman, Portfolio selection with transaction costs. Math. Oper. Res. 15 (1990), 676-713.
9. P. Donnelly and T.G. Kurtz. Particle representations for measure-valued population models. Ann. Probab. 27 (1999), 166-205.
10. P.E. Echeverria, A criterion for invariant measures of Markov processes, Z. Wahrsch. verw. Gebiete 61 (1982), 1-16.
11. S.N. Ethier and T.G. Kurtz, Markov Processes: Characterization and Convergence, Wiley, New York (1986).
12. J. Jacod and A.N. Shiryaev, Limit Theorems for Stochastic Processes, Springer-Verlag, Berlin (1987).
13. A. Jakubowski, A non-Skorohod topology on the Skorohod space. Electron. J. Probab. 2 (1997), paper no. 4, 21 pp.
14. I. Karatzas, A class of singular stochastic control problems. Adv. in Appl. Probab. 15 (1983), 225-254.
15. T.G. Kurtz, Martingale problems for constrained Markov processes, in Recent Advances in Stochastic Calculus, J.S. Baras, V. Mirelli, eds., Springer-Verlag, New York, 1990.
16. T.G. Kurtz, A control formulation for constrained Markov processes, in Mathematics of Random Media, Lectures in Applied Mathematics, 27, 1991.
17. T.G. Kurtz, Random time changes and convergence in distribution under the Meyer-Zheng conditions, Ann. Probab., 19 (1991), 1010-1034.
18. T.G. Kurtz, Averaging for martingale problems and stochastic approximation, Proceedings of the Joint U.S.-French Workshop on Applied Stochastic Analysis. Springer Lecture Notes in Control and Inf. Sci. 177 (1992), 186-209.
19. T.G. Kurtz. Martingale problems for conditional distributions of Markov processes. Electron. J. Probab. 3 (1998), Paper 9, 29 pp.
20. T.G. Kurtz and D.L. Ocone. Unique characterization of conditional distributions in nonlinear filtering. Ann. Probab. 16 (1988), no. 1, 80-107.
21. T.G. Kurtz and R.H. Stockbridge, Existence of Markov controls and characterization of optimal Markov controls, SIAM J. Control Optim. 36 (1998), 609-653.
22. T.G. Kurtz and R.H. Stockbridge, Martingale problems and linear programs for singular control, Thirty-seventh annual Allerton conference on communication, control, and computing (Monticello, Ill., 1999), 11-20, Univ. Illinois, Urbana-Champaign, 1ll.
23. H.L. Royden, Real Analysis, 2nd ed., MacMillan, New York, 1968.
24. S.E. Shreve, An introduction to singular stochastic control. Stochastic differential systems, stochastic control theory and applications (Minneapolis, Minn., 1986), 513-528, IMA Vol. Math. Appl., 10, Springer, New York-Berlin, 1988.
25. S.E. Shreve and H.M. Soner, Optimal investment and consumption with transaction costs. Ann. Appl. Probab. 4 (1994), 609-692.
26. H.M. Soner and S.E. Shreve, Regularity of the value function for a two-dimensional singular stochastic control problem. SIAM J. Control Optim. 27 (1989), 876-907.
27. R.H. Stockbridge, Time-average control of martingale problems: Existence of a stationary solution, Ann. Probab. 18 (1990), 190-205.
28. R.H. Stockbridge, Time-average control of martingale problems: A linear programming formulation, Ann.. Probab. 18 (1990), 206-217.
29. A. Weiss, Invariant measures of diffusions in bounded domains, Ph.D. dissertation, New York University, 1981.