An Implicit Euler Scheme with Non-uniform Time Discretization for Heat Equations with Multiplicative Noise
نویسنده
چکیده
We present an algorithm for solving stochastic heat equations, whose key ingredient is a non-uniform time discretization of the driving Brownian motion W . For this algorithm we derive an error bound in terms of its number of evaluations of onedimensional components of W . The rate of convergence depends on the spatial dimension of the heat equation and on the decay of the eigenfunctions of the covariance of W . According to known lower bounds, our algorithm is optimal, up to a constant, and this optimality cannot be achieved by uniform time discretizations.
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