Authors
A Ya Dorogovtsev, SD Ivasishen, AG Kukush
Publication date
1985/1
Journal
Ukrainian Mathematical Journal
Volume
37
Pages
10-15
Publisher
Kluwer Academic Publishers-Plenum Publishers
Description
Here,{w (t)} is a standard Wiener process, matched with the flow of a-algebras {~ t};~ is a nonrandom measurable function of three variables. Two, in principle, different approaches are possible to the mathematically correct statement of problem (I)-(3). One consists in replacing Eq.(I) by a stochastic integral equation, containing a Green's function [I]. With the other approach, Eq.(I) is treated as a stochastic Ito equation with phase space L2 [0, I] and an unbounded transfer operator [2] or as an Ito equation with the space of generalized functions asthe phase space and a bounded transfer operator [3]. Let us give the relevant definitions.
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Scholar articles
AY Dorogovtsev, SD Ivasishen, AG Kukush - Ukrainian Mathematical Journal, 1985