4 papers
Central Limit Theorem for ergodic averages of Markov chains \& the comparison of sampling algorithms for heavy-tailed distributions
Miha BreÅ¡ar, Aleksandar MijatoviÄ, Gareth Roberts
Establishing central limit theorems (CLTs) for ergodic averages of Markov chains is a fundamental problem in probability and its applications. Since the seminal work~\cite{MR834478…
Stability of storage processes with general release rates
Miha BreÅ¡ar, Aleksandar MijatoviÄ, Nikola SandriÄ
This paper quantifies the ergodicity and the rate of decay of the tail of the stationary distribution for a broad class of storage models, encompassing constant, linear, and power-…
Non-asymptotic bounds for forward processes in denoising diffusions: Ornstein-Uhlenbeck is hard to beat
Miha BreÅ¡ar, Aleksandar MijatoviÄ
Denoising diffusion probabilistic models (DDPMs) represent a recent advance in generative modelling that has delivered state-of-the-art results across many domains of applications.…
Superdiffusive limits for Bessel-driven stochastic kinetics
Miha BreÅ¡ar, Conrado da Costa, Aleksandar MijatoviÄ +1
We prove anomalous-diffusion scaling for a one-dimensional stochastic kinetic dynamics, in which the stochastic drift is driven by an exogenous Bessel noise, and also includes endo…