Direct Numerical Solutions to Stochastic Differential Equations with Multiplicative Noise

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 multipli...

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Bibliographic Details
Published in:arXiv.org 2023-12
Main Authors: Grimm, Ryan T, Eaves, Joel D
Format: Article
Language:English
Subjects:
Differential equations
Numerical methods
Oscillators
Tensors
Online Access:Get full text
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Summary: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.
ISSN:2331-8422