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On equivalence of a process of diffusion type in Hilbert space and a Wiener process. (Russian) Zbl 0702.60069
The equivalence of a random process \(\xi\) (t) with values in a separable Hilbert space and a Wiener process W(t) defined on a finite interval \(<0,T>\) is proved in the case that \[ \xi (t)=\int^{t}_{0}A(s)\xi (s)ds+W(t),\quad 0\leq t\leq T, \] where A(s) is a measurable operator function satisfying \(\int^{T}_{0}| A(s)|^ 2ds<\infty\).
Reviewer: D.Jaruškova
MSC:
60J60 Diffusion processes
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60J65 Brownian motion
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