Well-posedness and stationary distribution of free stochastic differential equations

Jiaxin Wei; Zhi Yin

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arXiv · 2606.31528

Well-posedness and stationary distribution of free stochastic differential equations

Jiaxin Wei·Zhi Yin

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Abstract

This paper studies free stochastic differential equations driven by free Brownian motion. Under local operator Lipschitz and Lyapunov-type conditions on the coefficients, we prove the global well-posedness of solutions in the noncommutative probability setting using free It\^o calculus. We further establish the existence and uniqueness of stationary solutions under appropriate dissipativity conditions. Our results extend classical theory to the free probability framework.

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Jiaxin Wei, Zhi Yin. 2026-06-30. Well-posedness and stationary distribution of free stochastic differential equations. https://arxiv.org/abs/2606.31528

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