- Random branching and affine structures
- Affine stochastic recursions, Lipschitz iterations, global and local regularity of stationary measures.
- Perpetuities, their path properties and related large deviations.
- Multivariate stochastic models with power law tails.
- Univariate and multivariate smoothing transforms.
- Branching processes in random environment.
Harmonic functions on solvable NA groups
- Theory of Poisson-Furstenberg boundaries for Hörmander type left-invariant differential operators on NA groups.
- Analysis on harmonic manifolds.
- Sharp pointwise estimates for Green functions and Poisson kernels for left-invariant differential operators on homogeneous manifolds of negative curvature. Estimates for derivatives of Poisson kernels.
- Study of non-coercive Hörmander type left-invariant differential operators on homogeneous manifolds of negative curvature. Martin boundary at the bottom of the spectrum.
- Analysis on homogeneous Siegel domains and Riemannian symmetric spaces of tube type
- Alternative Poisson kernels reproducing holomorphic functions on homogeneous Siegel domains. Hua - harmonic functions on homogeneous Siegel domains.
- Functions harmonic with respect to invariant systems of operators on symmetric Siegel domains with (or without) extra growth conditions and boundary smoothness.
- Characterization of pluriharmonic functions on symmetric Siegel domains as zeros of small systems of invariant operators.
- Complete characterization of Hua-harmonic functions on Siegel type two domains.
- Hua system on Riemannian symmetric spaces of tube type.