Let H be a separable Hilbert space. Suppose (Ω, F, Ft, P) is a complete stochastic basis with a right continuous filtration and {Wt,t ∈ R} is an H-valued cylindrical Brownian motion with respect to {Ω, F, Ft, P). U(t, s) denotes an almost strong evolution operator generated by a family of unbounded closed linear operators on H. Consider the semilinear stochastic integral equation
[formula omitted]
where
• f is of monotone type, i.e., ft(.) = f(t, w,.) : H → H is semimonotone, demicon-tinuous, uniformly bounded, and for each x ∈ H, ft(x) is a stochastic process which satisfies certain measurability conditions.
• gs(.) is a uniformly-Lipschitz predictable functional with values in the space of Hilbert-Schmidt operators on H.
• Vt is a cadlag adapted process with values in H.
• X₀ is a random variable.
We obtain existence, uniqueness, boundedness of the solution of this equation. We show the solution of this equation changes continuously when one or all of X₀, f, g, and V are varied. We apply this result to find stationary solutions of certain equations, and to study the associated large deviation principles.
Let {Zt,t ∈ R} be an H-valued semimartingale. We prove an Ito-type inequality and a Burkholder-type inequality for stochastic convolution [formula omitted]. These are the main tools for our study of the above stochastic integral equation. / Science, Faculty of / Mathematics, Department of / Graduate
| Identifer | oai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/31117 |
| Date | January 1990 |
| Creators | Zangeneh, Bijan Z. |
| Publisher | University of British Columbia |
| Source Sets | University of British Columbia |
| Language | English |
| Detected Language | English |
| Type | Text, Thesis/Dissertation |
| Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
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