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Lattice approximations for stochastic quasi-linear parabolic partial differential equations driven by space-time white noise. I. (English) Zbl 0915.60069
Summary: We approximate quasi-linear parabolic SPDEs substituting the derivatives in the space variable with finite differences. When the nonlinear terms in the equation are Lipschitz continuous, we estimate the rate of \(L^p\) convergence of the approximations and we also prove their almost sure uniform convergence to the solution. When the nonlinear terms are not Lipschitz continuous, we obtain this convergence in probability, if the pathwise uniqueness for the equation holds.

MSC:
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35R30 Inverse problems for PDEs
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