18 citations · 43 across the 23 of their papers we have counts for
5 papers · 1 filter
Lift zonoid order and functional inequalities
Alexei M. Kulik, Taras D. Tymoshkevych
We introduce the notion of a weighted lift zonoid and show that, for properly chosen weights v, the ordering condition on a measure μ, formulated in terms of the weighted lift zono…
Intrinsic compound kernel estimates for the transition probability density of a Lévy type processes and their applications
Victoria P. Knopova, Alexei M. Kulik
In this paper we construct the fundamental solution to some integro-differential equation, as well as the intrinsic upper and lower estimates for this solution. As an application o…
Parametrix construction for certain Lévy-type processes
Victoria Knopova, Alexei Kulik
In this paper we show that a non-local operator of certain type extends to the generator of a strong Markov process, admitting the transition probability density. For this transiti…
Poincare inequality and exponential integrability of the hitting times of a Markov process
Alexei M. Kulik
Extending the approach of the paper [Mathieu, P. (1997) Hitting times and spectral gap inequalities, Ann. Inst. Henri Poincare 33, 4, 437 -- 465], we prove that the Poincare inequa…
Malliavin calculus approach to statistical inference for Levy driven SDE's
D. O. Ivanenko, A. M. Kulik
By means of the Malliavin calculus, integral representations for the likelihood function and for the derivative of the log-likelihood function are given for a model based on discre…