Relation Between Stochastic Integrals the Geometry of Banach Spaces

Please enable javascript in your browser.

Rashtian, Hanif |

993 Viewed

Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 44010 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Zohuri Zangeneh, Bijan
Abstract:
n this article, we find necessary conditions for the existence of Ito Integral in a Banach space with respect to compensated Poisson random measure (cPrm). Ito integrals with values on M-type 2 Banach spaces F of the above form exist for all measurable, adapted functions f square integrable w.r.t. β ⊗ d t (f ∈ M2T;_(E/F)),with β being Lévy measure associated with cPrm, and have strong second moments. We show that, for general separable Banach spaces F, an inequality of the type resulting for M-type 2 Banach spaces with constant depending on cPrm is necessary and sufficient for the existence of Ito integral having second moment finite for all f ∈ M2 T;_(E/F). It is shown that M2 T;_(E/F) is the appropriate space in case F = H, is a separable Hilbert space. In addition, if the constant is independent of cPrm for all non-random functions inM2 T;_(E/F), then the Banach space is of type
Keywords:
Compensated Poisson Random Measures ; Martingale Type 2 Banach Spaces ; Stochastic Integral on Separable Hilbert and Banach Spaces ; Pettis and Ito Integrals