Using the coupling method to study stability of time-inhomogeneous Markov chains (presentation of the D.Sc. degree thesis)

Abstract: We consider a problem of geometric recurrence for a time-inhomogeneous Markov chain. A modified drift condition that guarantees such recurrence has been obtained. In addition, we derived conditions for geometric recurrence for the pair of chains. We applied these results to obtain estimates for the stability of a pair of time-inhomogeneous autoregressive Markov chains. We have also generalized Lindvall theorem for the finiteness of the expectation of a coupling time to a case of a coupling time for two different, time-inhomogeneous Markov chains and derived estimates for such expectation.

Ukrainianprobability

Audience: researchers in the discipline

Семінар з фрактального аналізу / Fractal analysis seminar

Series comments: Weekly research seminar on fractal analysis (online)

Topics:

• theory of fractals (fractal geometry and fractal analysis)
• Hausdorff–Besicovitch dimension, techniques and methods for its calculation and estimation
• functions and transformations preserving fractal (Hausdorff–Besicovitch, entropic, box-counting, packing, etc.) dimension
• sets of metric spaces that are essential for functions, sets, and dynamical systems
• self-similar, self-affine properties of mathematical objects
• systems of encoding for real numbers (numeral systems) and their applications
• metric number theory and metric theory of representations of numbers
• probabilistic number theory and probabilistic theory of representations of numbers
• measures supported on fractals, particularly singular measures and probability distributions
• nowhere monotonic and nowhere differentiable functions, functions with fractal properties
• theory of groups determined by invariants of transformations preserving tails of representation of numbers, digit frequencies, etc.

The talks are mostly in Ukrainian but English is also acceptable