2 citations · 2 across the 10 of their papers we have counts for
10 papers
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-…
Multivariate CLT for Lévy processes: convergence rates without moment assumptions
Jorge González Cázares, David Kramer-Bang, Aleksandar Mijatović
We prove that the norm of a -dimensional Lévy process possesses a finite second moment if and only if the convex distance between an appropriately rescaled process at time a…
Critical branching processes with immigration: scaling limits of local extinction sets
Aleksandar Mijatović, Benjamin Povar, Gerónimo Uribe Bravo
We establish the joint scaling limit of a critical Bienaymé-Galton-Watson process with immigration (BGWI) and its (counting) local time at zero to the corresponding self-similar co…
Central limit theorem for superdiffusive reflected Brownian motion
Aleksandar Mijatović, Isao Sauzedde, Andrew Wade
We study the second-order asymptotics around the superdiffusive strong law~\cite{MMW} of a multidimensional driftless diffusion with oblique reflection from the boundary in a gener…
Asymptotically optimal Wasserstein couplings for the small-time stable domain of attraction
Jorge González Cázares, David Kramer-Bang, Aleksandar Mijatović
We develop two novel couplings between general pure-jump Lévy processes in and apply them to obtain upper bounds on the rate of convergence in an appropriate Wasserstein dis…
Limit Theorems for Stochastic Gradient Descent with Infinite Variance
Jose Blanchet, Aleksandar Mijatović, Wenhao Yang
Stochastic gradient descent is a classic algorithm that has gained great popularity especially in the last decades as the most common approach for training models in machine learni…
Modeling of Measurement Error in Financial Returns Data
Ajay Jasra, Mohamed Maama, Aleksandar Mijatović
In this paper we consider the modeling of measurement error for fund returns data. In particular, given access to a time-series of discretely observed log-returns and the associate…
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…
Superdiffusive limits for stochastic kinetics driven by self-similar drifts
Miha Brešar, Conrado da Costa, Aleksandar Mijatović +1
We prove anomalous-diffusion scaling for a one-dimensional stochastic kinetic dynamics, in which the stochastic drift is driven by an exogenous self-similar noise, and also include…