摘要:

Multiple stochastic integral expansions are applied to the problem of filtering a signal observed in additive noise. It is shown that the optimal mean-square estimate may be represented as a ratio of two multiple integral series. A formula for expanding the product of two multiple integrals is developed and applied to deriving equations for the kernels of best, finite expansion approximations to the optimal filter. These equations are studied in detail in the quadratic case.

ISSN:0090-9491    

DOI:10.1080/17442508308833260

出版商:Gordon and Breach Science Publishers Inc    

年代:1983

数据来源: Taylor

摘要:

A probabilistic representation for the solution of a parabolic partial differential equation with uniformly elliptic diffusion coefficients but unbounded drift is obtained and some growth estimates are calculated. These are applied to prove uniqueness of solutions of a certain class of nonlinear filtering equations

ISSN:0090-9491    

DOI:10.1080/17442508308833261

出版商:Gordon and Breach Science Publishers Inc.    

年代:1983

数据来源: Taylor

摘要:

This article is concerned with the impulse control of stochastic systems, the internal state of which is only known by a noisy observation with both continuous and discontinuous components. It is shown that among the controls depending on the observation there exists an optimal one, that can be recursively constructed as a function of the filter associated with the system.

ISSN:0090-9491    

DOI:10.1080/17442508308833262

出版商:Gordon and Breach Science Publishers Inc    

年代:1983

数据来源: Taylor

摘要:

This paper contains some results about the theory of stochastic L2-Integration with a general time-region. The starting point of our theory is not a family of σ-algebras but, more generally, a family of projection operators in the Hilbert space of all square integrable random functions. To do this we use some Hilbert space analysis as well as the methods of Metivier and Pellaumail.

ISSN:0090-9491    

DOI:10.1080/17442508308833263

出版商:Gordon and Breach Science Publishers Inc    

年代:1983

数据来源: Taylor

ISSN:0090-9491    

DOI:10.1080/174425088308833259

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

年代:1983

数据来源: Taylor