58 citations · 395 across the 20 of their papers we have counts for
7 papers · 1 filter
A model of seasonal savanna dynamics
Paweł Klimasara, Marta Tyran-Kamińska
We introduce a mathematical model of savanna vegetation dynamics. The usual approach of nonequilibrium ecology is extended by including the impact of wet and dry seasons. We presen…
Piecewise deterministic Markov processes in biological models
Ryszard Rudnicki, Marta Tyran-Kaminska
We present a short introduction into the framework of piecewise deterministic Markov processes. We illustrate the abstract mathematical setting with a series of examples related to…
Existence of invariant densities for semiflows with jumps
Weronika Biedrzycka, Marta Tyran-Kaminska
The problem of existence and uniqueness of absolutely continuous invariant measures for a class of piecewise deterministic Markov processes is investigated using the theory of subs…
Dynamic behavior of stochastic gene expression models in the presence of bursting
M. C. Mackey, M. Tyran-Kamińska, R. Yvinec
This paper considers the behavior of discrete and continuous mathematical models for gene expression in the presence of transcriptional/translational bursting. We treat this proble…
Functional limit theorems for linear processes in the domain of attraction of stable laws
Marta Tyran-Kaminska
We study functional limit theorems for linear type processes with short memory under the assumption that the innovations are dependent identically distributed random variables with…
Convergence to Lévy stable processes under some weak dependence conditions
Marta Tyran-Kaminska
For a strictly stationary sequence of random vectors in we study convergence of partial sum processes to Lévy stable process in the Skorohod space with -topolog…