FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2001, VOLUME 7, NUMBER 2, PAGES 351-371
V. G. Zadorozhnij
Abstract
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The formulae of the mean value and the second moment function
are obtained for the heat differential equation with
stochastic coefficient at the higher derivative,
stochastic initial condition and stochastic exterior
perturbation. The formulae do not contain the continual integral
and hold even for dependent stochastic processes. The expression
for the mean value of the solution generalizes the well-known
Poisson formula for the solution of the heat differential
equation.
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Last modified: October 31, 2001.