29 citations · 33 across the 3 of their papers we have counts for
7 papers
Substochastic semigroups and densities of piecewise deterministic Markov processes
Marta Tyran-Kaminska
Necessary and sufficient conditions are given for a substochastic semigroup on obtained through the Kato--Voigt perturbation theorem to be either stochastic or strongly stabl…
Dynamics and density evolution in piecewise deterministic growth processes
Michael C. Mackey, Marta Tyran-Kaminska
A new sufficient condition is proved for the existence of stochastic semigroups generated by the sum of two unbounded operators. It is applied to one-dimensional piecewise determin…
Central Limit Theorems for Non-Invertible Measure Preserving Maps
Michael C. Mackey, Marta Tyran-Kaminska
We establish a new functional central limit theorem result for non-invertible measure preserving maps that are not necessarily ergodic, using the Perron-Frobenius operator. We appl…
Temporal Behavior of the Conditional and Gibbs' Entropies
Michael C. Mackey, Marta Tyran-Kaminska
We study the temporal approach to equilibrium of the Gibbs' and conditional entropies for both invertible deterministic dynamics as well as non-invertible stochastic systems in the…
Effects of Noise on Entropy Evolution
Michael C. Mackey, Marta Tyran-Kaminska
We study the convergence properties of the conditional (Kullback-Leibler) entropy in stochastic systems. We have proved very general results showing that asymptotic stability is a…
An invariance principle for maps with polynomial decay of correlations
Marta Tyran-Kaminska
We give a general method of deriving statistical limit theorems, such as the central limit theorem and its functional version, in the setting of ergodic measure preserving transfor…