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Title: A study of SPDEs w.r.t. compensated Poisson random measures and related topics
Author: Zhu, Jiahui
ISNI:       0000 0004 2749 5090
Awarding Body: University of York
Current Institution: University of York
Date of Award: 2010
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This thesis consists of two parts. In the first part, we define stochastic integrals w.r.t. the compensated Poisson random measures in a martingale type p, 1 ≤ p ≤ 2 Banach space and establish a certain continuity, in substitution of the Ita isometry property, for the stochastic integrals .. A version of Ita formula, as a generalization of the case studies in Ikecla and Watanabe [40], is derived. This Itô formula enables us to treat certain Levy processes without Gaussion components. Moreover, using ideas in [63] a version of stochastic Fubini theorem for stochastic integrals W.r. t. compensated Poisson random measures in martingale type spaces is established. In addition, if we assume that E is a martingale type p Banach space with the q-th, q ≥ p, power of the norm in C2-class, then we prove a maximal inequality for a cadlag modification u of the stochastic convolution w.r.t. the compensated Poisson random measures of a contraction Co-semigroups. The second part of this thesis is concerned with the existence and uniqueness of global mild solutions for stochastic beam equations w.r.t. the compensated Poisson random measures. In view of Khas'minskii's test for nonexplosions, the Lyapunov function technique is used via the Yosida approximation approach. Moreover, the asymptotic stability of the zero solution is proved and the Markov property of the solution is verified.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available