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Stochastic dynamical systems and processes with discontinuous sample paths
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Rogerson, Stephen John (1981) Stochastic dynamical systems and processes with discontinuous sample paths. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b1753219~S1
Abstract
Chapter 1 we use a Poisson stochastic measure to establish a method of localizing, and a change of chart formula for, a class of stochastic differential equations with discontinuous sample paths. This is based on Gikhman and Skorohod [4].
In Chapter 2 we use essentially the method of Elworthy [2], to construct a unique, maximal solution to a stochastic differential equation defined on a manifold M.
Chapter 3 establishes some properties of solutions of the equation. In particular if M is compact, then the solutions have infinite explosion time. We evaluate the infinitesimal generator of the process. By defining stochastic development of a-stable processes on the tangent space, we produce a process on the manifold which, as is shown in Section 6, is not a-stable on M.
| Item Type: | Thesis or Dissertation (PhD) | ||||
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| Subjects: | Q Science > QA Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Stochastic processes | ||||
| Official Date: | 1981 | ||||
| Dates: |
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| Institution: | University of Warwick | ||||
| Theses Department: | Mathematics Institute | ||||
| Thesis Type: | PhD | ||||
| Publication Status: | Unpublished | ||||
| Extent: | 81 leaves | ||||
| Language: | eng |
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