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The linear space of generalized Brownian motions with applications

Author: Jeong Hyun Lee
Journal: Proc. Amer. Math. Soc. 133 (2005), 2147-2155
MSC (2000): Primary 60J65, 28C20
Published electronically: January 31, 2005
MathSciNet review: 2137882
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Abstract: In this paper, we define, motivated by recent works of Chang and Skoug, stochastic integrals for a generalized Brownian motion ( ${\textrm{gBm}}$) $X$ and then use it to study the representation problem on the linear space $H(X)$ spanned by $X$. We next establish a translation theorem for $L^p$-functionals of $X$, $p \geq 1$, and then use this translation to establish an integration by parts formula for $L^p$-functionals of $X$.

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Additional Information

Jeong Hyun Lee
Affiliation: Department of Mathematics, Sogang University, Seoul 121-742, Korea
Address at time of publication: Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, New York 10012

Keywords: Generalized Brownian motion, translation theorem, directional derivative, integration by parts formula
Received by editor(s): January 20, 2004
Received by editor(s) in revised form: March 19, 2004
Published electronically: January 31, 2005
Additional Notes: This work was supported by Korea Research Foundation Grant (KRF-2003-015-C00065)
Communicated by: Richard C. Bradley
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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