Miha Brešar

I am an Assistant Professor in the School of Data Science at The Chinese University of Hong Kong, Shenzhen.

Previously, I was a Research Fellow in Statistics in the Department of Statistics at the University of Warwick. In January 2024, I defended my PhD thesis, which I completed under the supervision of Professor Aleksandar Mijatović at the University of Warwick.

I am recruiting Ph.D. students and postdocs with a strong background in Mathematics or ML/Stats. Please send your CV if interested to mihabresar (at) cuhk.edu.cn.

My research interest lie in probability theory and its applications.

Probability:

I specialize in stochastic analysis and Markov processes, focusing on:

Stochastic differential equations
Reflected Brownian motion
Ergodicity of Markov processes
Anomalous diffusions.

Applications:

The applied side of my research centres on the stability and convergence of stochastic algorithms, with particular emphasis on:

Markov Chain Monte Carlo
Denoising Diffusion Probabilistic Modelling

Research:

Central Limit Theorem for ergodic averages of Markov chains \& the comparison of sampling algorithms for heavy-tailed distributions (with Aleksandar Mijatović and Gareth Roberts), Submitted, 2025. [ArXiv]

Stability of storage processes with general release rates (with Aleksandar Mijatović and Nikola Sandrić), Submitted, 2025. [ArXiv]

Superdiffusive limits for Bessel-driven stochastic kinetics (with Conrado Da Costa, Aleksandar Mijatović and Andrew Wade), Submitted, 2024. [ArXiv]

Non-asymptotic bounds for forward processes in denoising diffusions: Ornstein-Uhlenbeck is hard to beat (with Aleksandar Mijatović), to appear in Annals of Applied Probability, [ArXiv]

Subexponential lower bounds for f -ergodic Markov processes (with Alekdandar Mijatović), to appear in Probability Theory and Related Fields (2024), 58pp., [ArXiv]

Brownian motion with asymptotically normal reflection in unbounded domains: from transience to stability (with Aleksandar Mijatović and Andrew Wade), Annals of Probability 53(1): 175-222 (2025), [ArXiv]