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Evaluation Formulas for Generalized Conditional Wiener Integrals with Drift on a Function Space
Author
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-11-02
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
Let C[0,t] denote a generalized Wiener space, the space of real-valued continuous functions on the interval [0,t] and define a stochastic process Y:C[0,t]×[0,t]→ℝ by Y(x,s)=∫0sh(u)dx(u)+a(s) for x∈C[0,t] and s∈[0,t], where h∈L2[0,t] with h≠0 a.e.
and a is continuous on [0,t].
Let random vectors Yn:C[0,t]→ℝn and Yn+1:C[0,t]→ℝn+1 be given by Yn(x)=(Y(x,t1),…,Y(x,tn)) and Yn+1(x)=(Y(x,t1),…,Y(x,tn),Y(x,tn+1)), where 0 In this paper we derive a translation theorem for a generalized Wiener integral and then prove that Y is a generalized Brownian motion process with drift a. Furthermore, we derive two simple formulas for generalized conditional Wiener integrals of functions on C[0,t] with the drift and the conditioning functions Yn and Yn+1. As applications of these simple formulas, we evaluate the generalized conditional Wiener integrals of various functions on C[0,t].
American Psychological Association (APA)
Cho, Dong Hyun. 2013. Evaluation Formulas for Generalized Conditional Wiener Integrals with Drift on a Function Space. Journal of Function Spaces،Vol. 2013, no. 2013, pp.1-9.
https://search.emarefa.net/detail/BIM-1006095
Modern Language Association (MLA)
Cho, Dong Hyun. Evaluation Formulas for Generalized Conditional Wiener Integrals with Drift on a Function Space. Journal of Function Spaces No. 2013 (2013), pp.1-9.
https://search.emarefa.net/detail/BIM-1006095
American Medical Association (AMA)
Cho, Dong Hyun. Evaluation Formulas for Generalized Conditional Wiener Integrals with Drift on a Function Space. Journal of Function Spaces. 2013. Vol. 2013, no. 2013, pp.1-9.
https://search.emarefa.net/detail/BIM-1006095
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1006095