摘要:

The stochastic control systemis investigated, where ƒ,gdepend on the past (XS)S≤tof the stateXt, and the controlutdepends on partial observationsy=(Yt) made at a fixed finite sequence of times and lying in a countable observation space. We show ihai for a wide class of functions ƒ,gand terminal cost there is always an optimal relaxed control, and in certain circumstances there is an optimal ordinary control. We work on a hyperfinite Loeb space (a very rich probability space constructed using Robinson's nonstandard analysis), where, with a fixed Brownian motion b we have an explicit solution to the above equation for each controlu. An optimal internal (i.e. nonstandard) control is easily obtained. We show that an internal controlUcorresponds naturally to a standard relaxed control v whose solution process is pathwise the same as that forU.

ISSN:0090-9491    

DOI:10.1080/17442508308833241

出版商:Gordon and Breach Science Publishers Inc    

年代:1983

数据来源: Taylor

摘要:

In this paper we study the asymptotic behavior of Finite State Markov Processes with rare transitions. We show how to construct a sequence of increasingly simplified models of a singularly perturbed FSMP and how to combine these aggregated models to produce an asymptotic approximation of the original process uniformly valid over [0, ∞).

ISSN:0090-9491    

DOI:10.1080/17442508308833242

出版商:Gordon and Breach Science Publishers Inc    

年代:1983

数据来源: Taylor

摘要:

If ƒ is the difference of two convex functions onRnandXis a semimartingale, then ƒ(X) is also a semimartingale. We study the converse in this paper.

ISSN:0090-9491    

DOI:10.1080/17442508308833243

出版商:Gordon and Breach Science Publishers Inc    

年代:1983

数据来源: Taylor

摘要:

We consider the diffusiondw in a domainDwhich contains a unique asymptotically stable critical point of the ODE. Using probabilistic estimates we prove the following: 1) The Principle eigenfunction of the differential generator for tghe processx(tconverges to a constant as ε→0, boundedly inDand uniformly on compacts. 2) If τDis the exit time ofx(t) fromD, then λτDconverges in distribution to an exponential random variable with mean 1.(λ is the principle eigenvalue). Both of these results were known previosuly in the special case of a gradient flow:. Our arguments apply in the general non-gradient case.

ISSN:0090-9491    

DOI:10.1080/17442508308833244

出版商:Gordon and Breach Science Publishers Inc    

年代:1983

数据来源: Taylor

ISSN:0090-9491    

DOI:10.1080/17442508308833240

出版商:Gordon and Breach Science Publishers S. A.    

年代:1983

数据来源: Taylor