摘要:

Letx(t) be a diffusion satisfying the stochastic differential equation. V.Beneš gave an explicit formula for the conditional density ofx(t) givenwhenw(·)is a Brownian process independent ofx(·). This result is extended and then applied to derive recursive filtering equations for estimating conditional momentsfor estimating polynomial functionals ofx(·), and for smoothing.

ISSN:0090-9491    

DOI:10.1080/17442508208833224

出版商:Gordon and Breach Science Publishers Inc    

年代:1982

数据来源: Taylor

摘要:

A continuous time stochastic system with linear dynamics and linear observation equation has to be steered in such a way that the current predicted miss distance of the state to a given hyperplane, evaluated by some cost functional over a finite time interval, is minimized. it is shown that in the class of all controls taking values in the unit cube and depending only on the past of the observation process, the optimal control is bang-bang and that the separation and certainty equivalence principles hold

ISSN:0090-9491    

DOI:10.1080/17442508208833225

出版商:Gordon and Breach Science Publishers Inc    

年代:1982

数据来源: Taylor

摘要:

It is well-known (see R. S. Lipster and A. N. Shiryayev [1]) that weak solutions of stochastic differential equations with a unit diffusion coefficient and a square integrable drift coefficient are the only processes the measure of which is absolutely continuous with respect to the Wiener measure. Using the results of R. J. Chitashvili and N. L. Lazrieva \2] it is shown that weak solutions of such equations with a "non-sticky" boundary are the only processes with a measure absolutely continuous with respect to the Wiener process modulus measure and the expression for the corresponding density is given.

ISSN:0090-9491    

DOI:10.1080/17442508208833226

出版商:Gordon and Breach Science Publishers Inc    

年代:1982

数据来源: Taylor

摘要:

This paper deals with shot noise models driven by various point processes. By means of an approximating step response function the distribution of the Poisson shot noise is obtained. The exponential response function case is studied as well, writing down explicit univariate and bivariate distributions. In this case also the crossing problem is analyzed and upcrossing and downcrossing rates are evaluated The last part of the paper is concerned with bivariate shot noise fields in circular regions of the plane, both at inner and boundary points.

ISSN:0090-9491    

DOI:10.1080/17442508208833227

出版商:Gordon and Breach Science Publishers, Inc    

年代:1982

数据来源: Taylor

摘要:

A linear parabolic partial differential equation describing the pathwise filter for a nondegenerate diffusion is changed, by an exponential substitution. into the dynamic programming equation of an optimal stochastic control problem. This substitution is applied to obtain results about the rate of decay asof solutions p(x,t)to the pathwise filter equation, and for solutions of the corresponding Zakai equation

ISSN:0090-9491    

DOI:10.1080/17442508208833228

出版商:Gordon and Breach Science Publishers Inc.    

年代:1982

数据来源: Taylor

ISSN:0090-9491    

DOI:10.1080/17442508208833223

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

年代:1982

数据来源: Taylor