# The value function in ergodic control of diffusion processes with partial observations II

Applicationes Mathematicae (2000)

- Volume: 27, Issue: 4, page 455-464
- ISSN: 1233-7234

## Access Full Article

top## Abstract

top## How to cite

topBorkar, Vivek. "The value function in ergodic control of diffusion processes with partial observations II." Applicationes Mathematicae 27.4 (2000): 455-464. <http://eudml.org/doc/219288>.

@article{Borkar2000,

abstract = {The problem of minimizing the ergodic or time-averaged cost for a controlled diffusion with partial observations can be recast as an equivalent control problem for the associated nonlinear filter. In analogy with the completely observed case, one may seek the value function for this problem as the vanishing discount limit of value functions for the associated discounted cost problems. This passage is justified here for the scalar case under a stability hypothesis, leading in particular to a "martingale" formulation of the dynamic programming principle.},

author = {Borkar, Vivek},

journal = {Applicationes Mathematicae},

keywords = {vanishing discount limit; value function; ergodic control; scalar diffusions; partial observations},

language = {eng},

number = {4},

pages = {455-464},

title = {The value function in ergodic control of diffusion processes with partial observations II},

url = {http://eudml.org/doc/219288},

volume = {27},

year = {2000},

}

TY - JOUR

AU - Borkar, Vivek

TI - The value function in ergodic control of diffusion processes with partial observations II

JO - Applicationes Mathematicae

PY - 2000

VL - 27

IS - 4

SP - 455

EP - 464

AB - The problem of minimizing the ergodic or time-averaged cost for a controlled diffusion with partial observations can be recast as an equivalent control problem for the associated nonlinear filter. In analogy with the completely observed case, one may seek the value function for this problem as the vanishing discount limit of value functions for the associated discounted cost problems. This passage is justified here for the scalar case under a stability hypothesis, leading in particular to a "martingale" formulation of the dynamic programming principle.

LA - eng

KW - vanishing discount limit; value function; ergodic control; scalar diffusions; partial observations

UR - http://eudml.org/doc/219288

ER -

## References

top- D. G. Aronson (1967), Bounds for the fundamental solution of a parabolic equation, Bull. Amer. Math. Soc. 73, 890-896. Zbl0153.42002
- G. K. Basak, V. S. Borkar and M. K. Ghosh (1997), Ergodic control of degenerate diffusions, Stochastic Anal. Appl. 15, 1-17. Zbl0872.93079
- A. G. Bhatt and V. S. Borkar (1996), Occupation measures for controlled Markov processes: characterization and optimality, Ann. Probab. 24, 1531-1562. Zbl0863.93086
- R. N. Bhattacharya (1981), Asymptotic behaviour of several dimensional diffusions, in: Stochastic Nonlinear Systems in Physics, Chemistry and Biology, L. Arnold and R. Lefever (eds.), Springer Ser. Synerg. 8, Springer, Berlin, 86-99.
- V. S. Borkar (1989), Optimal Control of Diffusion Processes, Pitman Res. Notes Math. Ser. 203, Longman Sci. and Tech., Harlow. Zbl0669.93065
- V. S. Borkar (1999), The value function in ergodic control of diffusion processes with partial observations, Stochastics Stochastics Reports 67, 255-266. Zbl0947.93038
- W. F. Fleming and E. Pardoux (1982), Optimal control of partially observed diffusions, SIAM J. Control Optim. 20, 261-285. Zbl0484.93077
- N. Ikeda and S. Watanabe (1981), Stochastic Differential Equations and Diffusion Processes, North-Holland, Amsterdam, and Kodansha, Tokyo. Zbl0495.60005
- C. Striebel (1984), Martingale methods for the optimal control of continuous time stochastic systems, Stochastic Process. Appl. 18, 329-347.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.