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Keywords:

  • Necessary and sufficient conditions;
  • positive cone;
  • semi-linear parabolic systems;
  • stochastic PDEs.

Abstract

We study the positivity of solutions of a class of semi-linear parabolic systems of stochastic partial differential equations by considering random approximations. For the family of random approximations we derive explicit necessary and sufficient conditions such that the solutions preserve positivity. These conditions imply the positivity of the solutions of the stochastic system for both Itô's and Stratonovich's interpretation of stochastic differential equations.