On the convergence of partial differential equations of parabolic type with rapidly oscillating coefficients to stochastic partial differential equations
1989
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.
Keywords:
- Elliptic partial differential equation
- First-order partial differential equation
- Mathematical optimization
- Mathematical analysis
- Stochastic partial differential equation
- Mathematics
- FTCS scheme
- Numerical partial differential equations
- Separable partial differential equation
- Symbol of a differential operator
- Parabolic partial differential equation
- Differential equation
- Hyperbolic partial differential equation
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