White Noise Generalization of the Clark-Ocone Formula Under Change of Measure

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2010-01-01

Author

Okur, Yeliz Yolcu

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We prove the white noise generalization of the Clark-Ocone formula under change of measure by using Gaussian white noise analysis and Malliavin calculus. Let W(t) be a Brownian motion on the filtered white noise probability space (Omega, B, {F(t)}(0 <= t <= T), P) and let (W) over cap (t) be defined as d (W) over cap (t) = u(t)dt + dW (t), where u W(t) is an F(t)-measurable process satisfying certain conditions for all 0 <= t <= T. Let Q be the probability measure equivalent to P such that (W) over cap is a Brownian motion with respect to Q, in virtue of the Girsanov theorem. In this article, it is shown that for any square integrable F(T)-measurable random variable,

Subject Keywords

Statistics, Probability and Uncertainty, Statistics and Probability, Applied Mathematics

URI

https://hdl.handle.net/11511/63792

Journal

STOCHASTIC ANALYSIS AND APPLICATIONS

DOI

https://doi.org/10.1080/07362994.2010.515498

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Graduate School of Applied Mathematics, Article

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Citation Formats

Y. Y. Okur, “White Noise Generalization of the Clark-Ocone Formula Under Change of Measure,” STOCHASTIC ANALYSIS AND APPLICATIONS, pp. 1106–1121, 2010, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/63792.