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- Interdisciplinary Centre for Security, Reliability and TrustLU193 papers
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14 papers · 2 filters
Functional inequalities on manifolds with non-convex boundary
Li-Juan Cheng, Anton Thalmaier, James Thompson
In this article, new curvature conditions are introduced to establish functional inequalities including gradient estimates, Harnack inequalities and transportation-cost inequalitie…
Functional approximations with Stein's method of exchangeable pairs
Mikolaj J. Kasprzak
We combine the method of exchangeable pairs with Stein's method for functional approximation. As a result, we give a general linearity condition under which an abstract Gaussian ap…
Time Averages of Markov Processes and Applications to Two-Timescale Problems
Bob Pepin
We show a decomposition into the sum of a martingale and a deterministic quantity for time averages of the solutions to non-autonomous SDEs and for discrete-time Markov processes.…
Towards a Quantitative Averaging Principle for Stochastic Differential Equations
Bob Pepin
This work explores the use of a forward-backward martingale method together with a decoupling argument and entropic estimates between the conditional and averaged measures to prove…
Evolution systems of measures and semigroup properties on evolving manifolds
Li-Juan Cheng, Anton Thalmaier
An evolving Riemannian manifold consists of a smooth -dimensional manifold , equipped with a geometric flow of complete Riemannian metrics, parametri…
Stein's method for multivariate Brownian approximations of sums under dependence
Mikołaj J. Kasprzak
We use Stein's method to obtain a bound on the distance between scaled -dimensional random walks and a -dimensional (correlated) Brownian Motion. We consider dependence schem…