Controlled diffusions with boundary-crossing costs

Borkar, Vivek S.

doi:10.1007/bf01443615

Cited by 5 publications

(2 citation statements)

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“…Let d=l, S=(-1,11, a(') a 1, F(x,y) = y for all x, and the cost functional [20] to prove that g(x,') remains equicontinuous bounded on compact subsets of G\{x}. It is not hard to deduce from this that the attainable g(x,') form a compact set C x in C(G\{x}) and the bijection yx --g(x,') is a homeomorphism between Mx and Cx.…”

Section: Remarksmentioning

confidence: 99%

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The probabilistic structure of controlled diffusion processes

Borkar

1988

Acta Appl Math

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This paper surveys those aspects of controlled diffusion processes wherein the control problem is treated as an optimization problem on a set of probability measures on the path space.This includes: (i) existence results for optimal admissible or Markov controls (both in nondegenerate and degenerate cases),(ii) a probabilistic treatment of the dynamic programming principle, (iii) the corresponding results for control under partial observations, (iv) a probabilistic approach to the ergodic control problem. The paper is expository in nature and aims at giving a unified treatment of several old and new results that evolve around certain central ideas.

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Section: Remarksmentioning

confidence: 99%

“…An example is the functional fg(x,y)h(dy) where h is a finite measure supported on the boundary of a subdomain of G which is bounded away from x, having the interpretation as a 'boundary-crossing cost' [20].…”

Section: Remarksmentioning

confidence: 99%