摘要:

Two types of equations are considered:where A is a predictable increasing process, M is a locally square integrable martingale taking values in a Hilbert space, q is a stochastic martingale measure, a,b,c are random functions continuous in x which satisfy natural measurability properties, a kind of monotonity condition and a condition on growth in x. (Thaese are weaker than the usual Lipschitz condition and the condition of linear growth in x, respectively.) A uniqueness and exixtence theorem is proved for the solutions (which take values in Rd) of Eq. (1). It is shown that Eq. (2) Can be rewritten into the form of Eq.(1), and so the uniqueness and existence theorem is obtained for Eq.(2) as well. Further, the dependence of the solutions on parameters and initial values are investigated. The proffs are elementary and are based on the methods used in [8].

ISSN:0090-9491    

DOI:10.1080/03610918008833154

出版商:Gordon and Breach Science Publishers, Inc    

年代:1980

数据来源: Taylor

摘要:

We consider the following stochastic differentic equationwhereZis a given semimartingale andKis a given process with right-continuous and lefthand limited paths, on some filtered probability space. We prove the exixtence of a strong solution (or: solution-process) on this space, under an at most linear growth condition on g, when the usual Lipschitz Countinuity ofg,(ω,x) inxis replaced by weaker hypothese, namely that gs(ω,x) is continuous inxand satisfies a monotonicity condition related to the processZ.

ISSN:0090-9491    

DOI:10.1080/17442508008833155

出版商:Gordon and Breach Science Publishers, Inc    

年代:1980

数据来源: Taylor

摘要:

We find the explicit solution to several new problems in stochastic control, among them the finite-fuel problem of optimally tracking a standard Wiener processx+wtstarted atxby a nonanticipating process ξthaving ξ0=0 and total variation (fuel)so as to minimize the expected discounted cost. In n dimensions, the optimal process ξ is given thus: fuel is expended in a singular way to forcex+w–ξtreach and stay in the regionremaining at timet, and f′ is a Bessel (n even) or an elementary function (n odd). Except for a possible initial jump in ξ the processis a degenerate diffusion that reflects at fixed angels off the boundaryand is expressible in terms of the local times on the boundary components.

ISSN:0090-9491    

DOI:10.1080/17442508008833156

出版商:Gordon and Breach Science Publishers, Inc    

年代:1980

数据来源: Taylor