An extension of Wiener integration with the use of operator theory

Details An extension of Wiener integration with the use of operator theory An extension of Wiener integration with the use of operator theory

2009-01-01

arxiv.org/abs/0901.0195v1

Physics

Mathematical Physics

13 pages

Scientific paper

With the use of tensor product of Hilbert space, and a diagonalization procedure from operator theory, we derive an approximation formula for a general class of stochastic integrals. Further we establish a generalized Fourier expansion for these stochastic integrals. In our extension, we circumvent some of the limitations of the more widely used stochastic integral due to Wiener and Ito, i.e., stochastic integration with respect to Brownian motion. Finally we discuss the connection between the two approaches, as well as a priori estimates and applications.

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