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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

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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)
Subjects: Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH): Stochastic processes
Official Date: 1981
Dates:
DateEvent
1981Submitted
Institution: University of Warwick
Theses Department: Mathematics Institute
Thesis Type: PhD
Publication Status: Unpublished
Extent: 81 leaves
Language: eng

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