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arXiv · 2312.05507

Direct Numerical Solutions to Stochastic Differential Equations with Multiplicative Noise

Ryan T. Grimm·Joel D. Eaves
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Abstract

Inspired by path-integral solutions to the quantum relaxation problem, we develop a numerical method to solve classical stochastic differential equations with multiplicative noise that avoids averaging over trajectories. To test the method, we simulate the dynamics of a classical oscillator multiplicatively coupled to non-Markovian noise. When accelerated using tensor factorization techniques, it accurately estimates the transition into the bifurcation regime of the oscillator and outperforms trajectory-averaging simulations with a computational cost that is orders of magnitude lower.

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BibTeXRIS

Ryan T. Grimm, Joel D. Eaves. 2023-12-09. Direct Numerical Solutions to Stochastic Differential Equations with Multiplicative Noise. https://arxiv.org/abs/2312.05507

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