摘要:

The classBof strong solutions of the boundary problem for a stochastic differential equation with given drift and diffusion coefficients implies here a class of all continuous processes having the given stochastic differential within the interval [y1,y2] and not leaving it. It is shown that the classBcan be characterized as a class of all solutions of some stochastic integral equation. The instantly reflecting process (IRP) in A. Skorokhod's sense is proved to be the extremal (with respect to some ordering) element of this class and in the case when the drift and diffusion coefficients satisfy the Lipschitz condition it can be constructed by the method of successive approximations. The convergence of discrete approximations, which are constructed by the natural analogy of Euler's formula to the IRP, is studied.

ISSN:0090-9491    

DOI:10.1080/17442508108833184

出版商:Gordon and Breach Science Publishers Inc    

年代:1981

数据来源: Taylor

摘要:

In this paper we obtain the solution of a class of nonlinear filtering problems in the form of a series expansion in terms of multiple Wiener integrals. The solution is explicit in the sense that the kernels of the integrals in the expansion are explicitly determine.

ISSN:0090-9491    

DOI:10.1080/17442508108833185

出版商:Gordon and Breach Science Publishers Inc    

年代:1981

数据来源: Taylor

摘要:

For a stochastic processX= {Xn,n≥0} adapted to a given filtration, the predictable transform ofXby a predictable processV={Vn,n≥0} is defined to bewhen this sum makes sense. The problem of maximisingEV*Xover the classes of predictable processesVfor which either, is considered. It is shown that the form of the solution to the problem depends on whetherp≤1 orP>1.

ISSN:0090-9491    

DOI:10.1080/17442508108833186

出版商:Gordon and Breach Science Publishers Inc    

年代:1981

数据来源: Taylor

ISSN:0090-9491    

DOI:10.1080/1744259108833183

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

年代:1981

数据来源: Taylor