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arXiv · 1504.06149

A low-rank approach to the computation of path integrals

M. S. Litsarev·I. V. Oseledets
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Abstract

We present a method for solving the reaction-diffusion equation with general potential in free space. It is based on the approximation of the Feynman-Kac formula by a sequence of convolutions on sequentially diminishing grids. For computation of the convolutions we propose a fast algorithm based on the low-rank approximation of the Hankel matrices. The algorithm has complexity of $\mathcal{O}(nr M \log M + nr^2 M)$ flops and requires $\mathcal{O}(M r)$ floating-point numbers in memory, where $n$ is the dimension of the integral, $r \ll n$, and $M$ is the mesh size in one dimension. The presented technique can be generalized to the higher-order diffusion processes.

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M. S. Litsarev, I. V. Oseledets. 2015-04-22. A low-rank approach to the computation of path integrals. https://doi.org/10.1016/j.jcp.2015.11.009

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