Studying analytic and algebraic properties of probability measures
on locally compact topological groups, Lie groups.
Proving (central) limit theorems for triangular arrays of
probability measures defined on the above mentioned structures.
Constructing and studying bridges derived from Markov processes.
Especially, Wiener bridges, Bessel bridges, Ornstein-Uhlenbeck bridges.
Radial part of Markov processes.
Inhomogeneous diffusion processes: parameter estimation, explicit forms of Laplace transforms,
equivalence and singularity of probability measures induced by processes admitting
Theory of integer-valued time series: INAR models.
- Branching processes and affine processes: ergodicity and statistical inference.