Estimate of a random field based on the trajectory of a point moving in it
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Abstract
We consider the stochastic differential equationdξ t =Γ(ξ t )dt+σ t (ξ t )dw t in Euclidean space, where Γ(x) is a Gaussian random field andw t is a standard Wiener process. Let f t ξ =σ{ξ s ,s≤t}. Equations are obtained for the conditional meansm t (x)=f t ξ } andB t (x, y)=M{Г(x)Г(y)|f t ξ }.
Keywords
Euclidean Space Random Field Wiener Process Gaussian Random Field Standard Wiener Process
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Literature cited
- 1.V. V. Baklan, “The integration of random functions with respect to a Wiener random measure,”Teor. Veroyat. i Mat. Stat.,29, 10–14 (1983).Google Scholar
- 2.I. I. Gihman and A. V. Skorohod,Stochastic Differential Equations and their Applications, Springer, New York (1972).Google Scholar
Copyright information
© Plenum Publishing Corporation 1991