Abstract
In this paper we consider the convergence of the solutions to a sequence of partial differential equations of parabolic type with rapidly oscillating coefficients to the solutions of a stochastic partial differential equation. We use the martingale method and the characteristic functional to prove that the martingale problem has a unique solution. Our emphasis is in treating strongly mixing noises.
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Watanabe, H. On the convergence of partial differential equations of parabolic type with rapidly oscillating coefficients to stochastic partial differential equations. Appl Math Optim 20, 81–96 (1989). https://doi.org/10.1007/BF01447648
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DOI: https://doi.org/10.1007/BF01447648