Conference Agenda
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Statistics for Stochastic Processes Location: 0.002 Session Chair: Fabian Mies | |
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Geometric ergodicity of Langevin dynamics and its discretizations Taras Schevchenko National University of Kyiv, Ukraine We study the Langevin stochastic differential equation and its discrete approximations: the Euler–Maruyama scheme, commonly referred to as the Unadjusted Langevin Algorithm (ULA), and direct sampling from the continuous-time process. We show that the ULA process is geometrically ergodic in $\mathbb{R}^d$ under suitable conditions and derive a corresponding drift condition using a Foster–Lyapunov test function. We then analyze time-inhomogeneous approximations with diminishing step sizes and establish geometric recurrence for both chains—the ULA and the directly sampled chain. | |
