Proves global well-posedness and unique stationary distributions for free SDEs under local Lipschitz, Lyapunov, and dissipativity conditions on coefficients using free Itô calculus.
A Free Stochastic Partial Differential Equation
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abstract
We get stationary solutions of a free stochastic partial differential equation. As an application, we prove equality of non-microstate and microstate free entropy dimensions under a Lipschitz like condition on conjugate variables, assuming also R^\omega\ embeddability. This includes an N-tuple of q-Gaussian random variables e.g. for |q|N\leq 0.13.
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Well-posedness and stationary distribution of free stochastic differential equations
Proves global well-posedness and unique stationary distributions for free SDEs under local Lipschitz, Lyapunov, and dissipativity conditions on coefficients using free Itô calculus.