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Stochastic Integration in Abstract Spaces
Joint Authors
Source
International Journal of Stochastic Analysis
Issue
Vol. 2010, Issue 2010 (31 Dec. 2010), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2010-08-16
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Abstract EN
We establish the existence of a stochastic integral in a nuclear space setting as follows.
Let E, F, and G be nuclear spaces which satisfy the following conditions: the spaces are reflexive, complete, bornological spaces such that their strong duals also satisfy these conditions.
Assume that there is a continuous bilinear mapping of E×F into G.
If H is an integrable, E-valued predictable process and X is an F-valued square integrable martingale, then there exists a G-valued process (∫HdX)t called the stochastic integral.
The Lebesgue space of these integrable processes is studied and convergence theorems are given.
Extensions to general locally convex spaces are presented.
American Psychological Association (APA)
Brooks, J. K.& Kozinski, J. T.. 2010. Stochastic Integration in Abstract Spaces. International Journal of Stochastic Analysis،Vol. 2010, no. 2010, pp.1-7.
https://search.emarefa.net/detail/BIM-455391
Modern Language Association (MLA)
Brooks, J. K.& Kozinski, J. T.. Stochastic Integration in Abstract Spaces. International Journal of Stochastic Analysis No. 2010 (2010), pp.1-7.
https://search.emarefa.net/detail/BIM-455391
American Medical Association (AMA)
Brooks, J. K.& Kozinski, J. T.. Stochastic Integration in Abstract Spaces. International Journal of Stochastic Analysis. 2010. Vol. 2010, no. 2010, pp.1-7.
https://search.emarefa.net/detail/BIM-455391
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-455391