Proves global well-posedness and unique stationary distributions for free SDEs under local Lipschitz, Lyapunov, and dissipativity conditions on coefficients using free Itô calculus.
Non-commutative martingale inequalities
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abstract
We prove the analogue of the classical Burkholder-Gundy inequalites for non-commutative martingales. As applications we give a characterization for an Ito-Clifford integral to be an $L^p$-martingale via its integrand, and then extend the Ito-Clifford integral theory in $L^2$, developed by Barnett, Streater and Wilde, to $L^p$ for all $1<p<\infty$. We include an appendix on the non-commutative analogue of the classical Fefferman duality between $H^1$ and $BMO$.
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2026 1verdicts
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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.