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Fredholm Determinant of an Integral Operator Driven by a Diffusion Process
Author
Source
Journal of Applied Mathematics and Stochastic Analysis
Issue
Vol. 2008, Issue 2008 (31 Dec. 2008), pp.1-17, 17 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2008-11-02
Country of Publication
Egypt
No. of Pages
17
Main Subjects
Abstract EN
This article aims to give a formula for differentiating, with respect to T, an expression of the form λ(T,x):=?x[f(XT)e−∫0TV(Xs)ds(det(I+KX,T))P], where p≥0 and X is a diffusion process starting from x, taking values in a manifold, and the expectation is taken with respect to the law of this process.
KX,T:L2([0,T)→ℝN)→L2([0,T)→ℝN) is a trace class operator defined by KX,Tf(s)=∫0TH(s∧t)Γ(X(t))f(t)dt, where H, Γ are locally Lipschitz, positive N×N matrices.
American Psychological Association (APA)
Lim, Adrian P. C.. 2008. Fredholm Determinant of an Integral Operator Driven by a Diffusion Process. Journal of Applied Mathematics and Stochastic Analysis،Vol. 2008, no. 2008, pp.1-17.
https://search.emarefa.net/detail/BIM-448137
Modern Language Association (MLA)
Lim, Adrian P. C.. Fredholm Determinant of an Integral Operator Driven by a Diffusion Process. Journal of Applied Mathematics and Stochastic Analysis No. 2008 (2008), pp.1-17.
https://search.emarefa.net/detail/BIM-448137
American Medical Association (AMA)
Lim, Adrian P. C.. Fredholm Determinant of an Integral Operator Driven by a Diffusion Process. Journal of Applied Mathematics and Stochastic Analysis. 2008. Vol. 2008, no. 2008, pp.1-17.
https://search.emarefa.net/detail/BIM-448137
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-448137