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Construction of a solution of a certain evolution equation

Published online by Cambridge University Press:  22 January 2016

Akinobu Shimizu
Akinobu Shimizu*
Affiliation:
Nagoya Institute of Technology
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Let us consider the stochastic differential equation,

with initial condition,

where Bt, t ≧ 0,is a one-dimensional Brownian motion, and Lxis a second order uniformly elliptic partial differential operator satisfying some additional conditions that will be described in §2. The existence and the uniqueness of solutions of the Cauchy problem have been established by B. L. Rozovskii [8].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 66 , May 1977 , pp. 23 - 36
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1977

References

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[7] Hida, T.; Analysis of Brownian functionals, Carleton University lecture notes, 1975.Google Scholar
[8] Rozovskii, B. L.; On stochastic differential equations with partial derivatives (in Russian), Math. Sb., Vol. 06 (138), No. 2 (1975), 314–341.Google Scholar