The linear space of generalized Brownian motions with applications
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- by Jeong Hyun Lee
- Proc. Amer. Math. Soc. 133 (2005), 2147-2155
- DOI: https://doi.org/10.1090/S0002-9939-05-07751-8
- Published electronically: January 31, 2005
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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 $X$.References
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Bibliographic 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
- Email: rouge@sogang.ac.kr
- 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
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 2147-2155
- MSC (2000): Primary 60J65, 28C20
- DOI: https://doi.org/10.1090/S0002-9939-05-07751-8
- MathSciNet review: 2137882