4 papers
Ergodic Central limit theorem for subgeometric Markov chains
Miha Brešar, Aleksandar Mijatović, Gareth Roberts
We establish verifiable necessary conditions for central limit theorems (CLTs) of ergodic averages of Markov chains on general state spaces. Our criteria are based on discrete-time…
Stability of storage processes with general release rates
Miha Brešar, Aleksandar Mijatović, Nikola Sandrić
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 Brešar, Aleksandar Mijatović
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.…
Subexponential lower bounds for -ergodic Markov processes
Miha Brešar, Aleksandar Mijatović
We provide a criterion for establishing lower bounds on the rate of convergence in -variation of a continuous-time ergodic Markov process to its invariant measure. The criterion…