FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2001, VOLUME 7, NUMBER 2, PAGES 351-371

**The moment functions for the solution of the heat
equation with stochastic coefficients**

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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published in Russian.

Location: http://mech.math.msu.su/~fpm/eng/k01/k012/k01204h.htm.

Last modified: October 31, 2001.