Markov Processes Associated With Fully Nondiagonal Systems of Parabolic Equations

Ya. Belopolskaya

2014, v.20, №3, 451-478

ABSTRACT

We construct a new probabilistic representation for a weak solution of the Cauchy problem for a system of fully nondiagonal linear parabolic equations. Namely, we derive a system of stochastic equations associated with the original problem and construct its solution in the form of averages of initial data.

Keywords: fully nondiagonal systems of parabolic equations,the Cauchy problem,diffusion processes,weak solutions,probabilistic representations

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