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- W1579794310 abstract "This paper studies questions of changes of variables in a class of hyperbolic stochastic partial differential equations in two variables driven by white noise. Two types of changes of variables are considered: naive changes of variables which do not involve a change of filtration, which affect the equation much as though it were deterministic, and changes of variables that do involve a change of filtration, such as time-reversals. In particular, if the process in reversed coordinates does satisfy an s.p.d.e., then we show how this s.p.d.e. is related to the original one. Time-reversals for the Brownian sheet and for equations with constant coefficients are considered in detail. A necessary and sufficient condition is provided under which the reversal of the solution to the simplest hyperbolic s.p.d.e. with certain random initial conditions again satisfies such an s.p.d.e. This yields a negative conclusion concerning the reversal in time of the solution to the stochastic wave equation (in one spatial dimension) driven by white noise." @default.
- W1579794310 created "2016-06-24" @default.
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- W1579794310 date "2002-01-01" @default.
- W1579794310 modified "2023-09-26" @default.
- W1579794310 title "Time-Reversal in Hyperbolic S.P.D.E.'s" @default.
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- W1579794310 doi "https://doi.org/10.1214/aop/1020107766" @default.
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