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2013•Infinite Dimensional Analysis Quantum Probability and Related TopicsOpen access

STOCHASTIC INTEGRATION WITH RESPECT TO THE CYLINDRICAL WIENER PROCESS VIA REGULARIZATION

Christian Olivera

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Abstract

Following the ideas of F. Russo and P. Vallois, we use the notion of forward integral to introduce a new stochastic integral respect to the cylindrical Wiener process. This integral is an extension of the classical integral. As an application, we prove existence of solution of a parabolic stochastic differential partial equation with anticipating stochastic initial date.

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What this paper is about

Following the ideas of F. Russo and P. Vallois, we use the notion of forward integral to introduce a new stochastic integral respect to the cylindrical Wiener process. This integral is an extension of the classical integral. As an application, we prove existence of solution of a parabolic stochastic differential partial equation with anticipating stochastic initial date.

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Available abstract

Following the ideas of F. Russo and P. Vallois, we use the notion of forward integral to introduce a new stochastic integral respect to the cylindrical Wiener process. This integral is an extension of the classical integral. As an application, we prove existence of solution of a parabolic stochastic differential partial equation with anticipating stochastic initial date.

Key concepts: Stratonovich integral, Stochastic integral, Stochastic differential equation, Mathematics, Wiener process, Regularization (linguistics), Integral equation, Stochastic process

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