Li, Xue-Mei (1992) Stochastic flows on noncompact manifolds. PhD thesis, University of Warwick.

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Abstract

Here we look at the existence of solution flows of stochastic differential equations on noncompact manifolds and the properties of the solutions in terms of the geometry and topology of the underlying manifold itself. We obtain some results on "strong p-completeness” given conditions on the derivative flow, and thus given suitable conditions on the coefficients of the stochastic differential equations. In particular a smooth flow of Brownian motion exists on submanifolds of Rn whose second fundamental forms are bounded. Another class of results we obtain is on homotopy vanishing given strong moment stability. We also have results on obstructions to moment stability by cohomology. Also we obtain formulae for d(eᴢᵗΔʰØ) for differential form Ø in terms of a martingale and the form itself, not just its derivative, extending Bismut’s formula.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Stochastic differential equations, Stochastic geometry, Manifolds (Mathematics), Brownian motion processes
Official Date:	1992
Dates:	Date Event 1992 UNSPECIFIED
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Elworthy, K. D.
Sponsors:	European Council
Extent:	ii, 148 leaves
Language:	eng

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