Stochastic Differential Equations on Noncommutative L2
نویسنده
چکیده
We prove that a class of stochastic differential equations with multiplicative noise has a unique solution in a noncommutative L2 space associated with a von Neumann algebra. As examples we consider usual L2 on a measure space, Hilbert-Schmidt operators and a hyperfinite II1-factor. A problem of finding an inverse of the solution is then discussed. Finally, we explain how a stochastic differential equation can be used to construct a heat kernel measure on an infinite dimensional group. Table of
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