摘要:

We consider a rather general type of linear stochastic partial differential equations (PDE's) with delays where stochastic integral terms with respect to Wiener proceses and random measures are present.

ISSN:0090-9491    

DOI:10.1080/17442508208833230

出版商:Gordon and Breach Science Publishers Inc,    

年代:1982

数据来源: Taylor

摘要:

The paper is devoted to strong solutions of stochastic integral equations with respect to semimartingales. We study existence (for non-Lipschitz coefficients) and asymptotic behaviour of strong solutions and obtain also a number of results on weak and square mean convergence of these solutions.

ISSN:0090-9491    

DOI:10.1080/17442508208833231

出版商:Gordon and Breach Science Publishers Inc,    

年代:1982

数据来源: Taylor

摘要:

The paper deals with a definition and an approximation of symmetric (Stratonovich) stochastic integralwith respect to Brownian motion B using the representation of a square‐integrable process X in the form. We show that a natural definition is possible provided a certain Hilbert‐Schmidt operator related to the kernel L is nuclear (trace class). Denote BΔa polygonal approximation of B corresponding to a partition Δ of [0,1] and. We prove thatandconverge in mean toas the mesh(the later case needs additional assumptionor non-randomness of L).

ISSN:0090-9491    

DOI:10.1080/17442508208833232

出版商:Gordon and Breach Science Publishers Inc,    

年代:1982

数据来源: Taylor

摘要:

On a fixed time interval [0,T] we considerwhereMis a square integrable martingale with values in a Hilbert spaceK,Φs(ω) suitable operators fromKtoH, another Hilbert space, andUtsis a mild evolution operator onH. Under the assumption that there is a β≧0 such thatwe prove a submartingale type inequality for that integral. As applicatins we show that it has a continuous version, ifMhas, or is cadlage ifMis calage, and we prove that it is stable under some additional assumption onUtsFinally we ontain an existence and uniquenss theorem for an SPDE.

ISSN:0090-9491    

DOI:10.1080/17442508208833233

出版商:Gordon and Breach Science Publishers Inc,    

年代:1982

数据来源: Taylor

摘要:

We consider the maximal flow through a randomly capacitated network. We show that the maximal flowFnbetween vertices 0 and ∞ on of the complete graph on {0.1.2.…,n –1∞}. whose edges (i.j) are directed from i to j if and only ifi<j, satisfiesnlFn→>E(B) almost surelv and in mean, asn→>∞: hereE(B) is the mean value of a typical edge capacity. This answers a question posed by Grimmett and Welsh [I].

ISSN:0090-9491    

DOI:10.1080/17442508208833234

出版商:Gordon and Breach Science Publishers Inc,    

年代:1982

数据来源: Taylor

ISSN:0090-9491    

DOI:10.1080/1744258208833229

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

年代:1982

数据来源: Taylor