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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.

MSC:

60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60G15 Gaussian processes
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[17] VANCOUVER, BC V6T1Z2 CANADA E-MAIL: walsh@math.ubc.ca
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