Time-reversal in hyperbolic s. p. d. e. ’s. (English) Zbl 1019.60063

The authors consider two types of changes of variables in a class of hyperbolic s.p.d.e.’s. Time-reversals for the Brownian sheet and for equations with constant coefficients are discussed in detail. A necessary and sufficient condition for the reversal in two coordinates to satisfy an s.p.d.e. with local coefficients is proved. This result 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.


60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60G15 Gaussian processes
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