Representations of mild solutions of time-varying linear stochastic equations and the exponential stability of periodic systems.
Research problems of Jerzy Zabczyk
In the paper we present a selected variety of problems studied by Professor Jerzy Zabczyk. Important part of Prof. Zabczyk's scientific activity was devoted to his PhD students. He has promoted 9 PhD students: Tomasz Bielecki, Jarosław Sobczyk, Łukasz Stettner and Gianmario Tessitore work mostly in control and its applications to mathematical finance, whereas the research of Anna Chojnowska-Michalik, Wojciech Jachimiak, Anna Milian, Szymon Peszat and Anna Rusinek is concentrated mostly on stochastic...
Resonant averaging for weakly nonlinear stochastic Schrödinger equations
Retarded functional differential equations with white noise perturbations
Riccati equations and delay-dependent BIBO stabilization of stochastic systems with mixed delays and nonlinear perturbations.
Riesz transforms : a simpler analytic proof of P. A. Meyer's inequality
Riesz transforms for symmetric diffusion operators on complete Riemannian manifolds.
Robust estimates of certain large deviation probabilities for controlled semi-martingales
Motivated by downside risk minimization on the wealth process in an incomplete market model, we have studied in the recent work the asymptotic behavior as time horizon T → ∞ of the minimizing probability that the empirical mean of a controlled semi-martingale falls below a certain level on the time horizon T. This asymptotic behavior relates to a risk-sensitive stochastic control problem in the risk-averse case. Indeed, we obtained an expression of the decay rate of the probability by the Legendre...
Robust Filtering for Correlated Multidimensional Oberservations.
Robust option replication for a Black-Scholes model extended with nondeterministic trends.
Rolling with “slipping” : I