My research focusses on stochastic analysis and its applications. In particular, I am working on the
qualitative behavior of stochastic dynamical systems such as systems of stochastic differential
equations (ordinary, partial, functional), their numerical methods and stochastic difference equations.
The applications range from mechanical engineering (random vibrations, oscillators), laser physics
(injection locking), finance (interest rates, dynamic asset pricing), marketing (innovation diffusion)
to biology and ecology (random epidemics, population models).
Selected Publications
Applications of numerical methods
and its analysis for systems of stochastic differential equations, Bull.
Karela Math. Soc. 4 (1) (2007), 1-85.
Existence and uniqueness of solutions
of semilinear stochastic infinite-dimensional differential systems with H-regular
noise, J. Math. Anal. Appl. 332 (1) (2007) 334-345.
An axiomatic approach to numerical
approximations of stochastic processes, Int. J. Numer. Anal. Model.
3 (4) (2006) 459-480.
Stochastic $\alpha$-calculus,
a fundamental theorem and Burkholder-Davis-Gundy-type estimates, Dynam.
Syst. Applic. 15 (2) (2006) 241-268.
Stability of numerical methods
for ordinary SDEs along Lyapunov-type and other functions with variable step
sizes, Electr. Trans. Numer. Anal. 20 (2005), p. 27-49.
Dissipation of mean energy of
discretized linear oscillators under random perturbations, Discrete Contin.
Dyn. Syst. (Suppl. Vol. 2005), p. 778-783, 2005.
Moment attractivity, stability
and contractivity exponents of stochastic dynamical systems, Discrete
Contin. Dyn. Syst. 7 (3), p. 487-515, 2001.
Stability, stationarity, and boundedness
of some implicit numerical methods for stochastic differential equations and
applications, Logos-Verlag, Berlin, pp. 288, 1997 (Research Monograph, ISBN
3-931216-94-2).