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math.PR2008
Conditions for existence and smoothness of the distribution density for an Ornstein-Uhlenbeck process with Levy noise
Semen V. Bodnarchuk, Alexey M. Kulik
Conditions are given, sufficient for the distribution of an Ornstein-Uhlenbeck process with Lévy noise to be absolutely continuous or to possess a smooth density. For the processes…
math.PR2007★ 6 cited
Invariance principle for additive functionals of Markov chains
Yuri N. Kartashov, Alexey M. Kulik
We consider a sequence of additive functionals {ϕ_n}, set on a sequence of Markov chains {X_n} that weakly converges to a Markov process X. We give sufficient condition for such a…
math.PR2007★ 2 cited
Exponential ergodicity of the solutions to SDE's with a jump noise
Alexey M. Kulik
The mild sufficient conditions for exponential ergodicity of a Markov process, defined as the solution to SDE with a jump noise, are given. These conditions include three principal…