Markov Processes Associated With Fully Nondiagonal Systems of Parabolic Equations
2014, v.20, Issue 3, 451-478
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