A Generalization of the Clark-Ocone Formula - Journal of Applied Mathematics and Physics

JAMP > Vol.6 No.7, July 2018

Journal of Applied Mathematics and Physics

Volume 6, Issue 7 (July 2018)

ISSN Print: 2327-4352 ISSN Online: 2327-4379

Google-based Impact Factor: 0.70 Citations

A Generalization of the Clark-Ocone Formula ()

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Download as PDF (Size: 419KB) PP. 1443-1453

DOI: 10.4236/jamp.2018.67121 575 Downloads 1,535 Views

Author(s)

Mahmmoud Salih^*, Sulieman Jomah

Affiliation(s)

School of Mathematics and Statistics, Northwest Normal University, Lanzhou, China.

ABSTRACT

In this paper, we use a white noise approach to Malliavin calculus to prove the generalization of the Clark-Ocone formula

, where E[F] denotes the generalized expectation,

is the (generalized) Malliavin derivative, ◊ is the Wick product and W(t) is the 1-dimensional Gaussian white noise.

KEYWORDS

White Noise, Malliavin Calculus, Wick Product, Brownian Motion

Share and Cite:

Salih, M. and Jomah, S. (2018) A Generalization of the Clark-Ocone Formula. Journal of Applied Mathematics and Physics, 6, 1443-1453. doi: 10.4236/jamp.2018.67121.

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