39 citations · 62 across the 18 of their papers we have counts for
21 papers
On ergodic property of the solution to a Lévy-driven SDE
Victoria Knopova, Yana Mokanu
In this paper, we investigate ergodicity in total variation of the process , related to a Lévy-driven stochastic differential equation with unbounded coefficients, and describ…
On ergodic properties of some Levy-type processes
Victoria Knopova, Yana Mokanu
In this note we prove some sufficient conditions for ergodicity of a Levy-type process, such that on the test functions the generator of the respective semigroup is of the form $$…
Construction and heat kernel estimates of general stable-like Markov processes
V. Knopova, A. Kulik, R. Schilling
A stable-like process is a Feller process taking values in and whose generator behaves, locally, like an -stable Lévy process, but the index …
Subexponential potential asymptotics with applications
Victoria Knopova, Zbigniew Palmowski
Let be a multivariate process of the form , , killed at some terminal time , where is a Markov process having only jumps of the length…
On the Liouville property for non-local Lévy generators
Victoria Knopova, René Schilling
We prove a necessary and sufficient condition for the Liouville property of the infinitesimal generator of a Lévy process and subordinate Lévy processes. Combining our criterion wi…
A Probabilistic proof of the breakdown of Besov regularity in -shaped domains
Victoria Knopova, René L. Schilling
{We provide a probabilistic approach in order to investigate the smoothness of the solution to the Poisson and Dirichlet problems in -shaped domains. In particular, we obtain (p…
Heat kernel of anisotropic nonlocal operators
Krzysztof Bogdan, Paweł Sztonyk, Victoria Knopova
We construct and estimate the fundamental solution of highly anisotropic space-inhomogeneous integro-differential operators. We use the Levi method. We give applications to the Cau…
On the Feynman--Kac semigroup for some Markov processes
Victoria Knopova
For a (non-symmetric) strong Markov process , consider the Feynman--Kac semigroup \[T_t^Af(x):=\mathbb {E}^x\bigl[e^{A_t}f(X_t)\bigr],\quad x\in {\mathbb {R}^n}, t>0,\] where $A…
Accuracy of discrete approximation for integral functionals of Markov processes
I. Ganychenko, V. Knopova, A. Kulik
The article is devoted to the estimation of the rate of convergence of integral functionals of a Markov process. Under the assumption that the given Markov process admits a transit…
Parametrix construction of the transition probability density of the solution to an SDE driven by -stable noise
Victoria Knopova, Alexei Kulik
Let , where , and $a:\rd\to (0,\infty)$, $b: \rd\to \rd$. Under certain regularity assumptions on the coefficients and , we…
On level and collision sets of some Feller processes
Victoria Knopova, René L. Schilling
This paper is about lower and upper bounds for the Hausdorff dimension of the level and collision sets of a class of Feller processes. Our approach is motivated by analogous result…
Lower Bounds of the Hausdorff dimension for Feller processes
Victoria Knopova, René L. Schilling, Jian Wang
Let be a Feller process generated by a pseudo-differential operator whose symbol satisfies and We prove t…
Compound kernel estimates for the transition probability density of a Lévy process in $\rn$
V. Knopova
We construct in the small-time setting the upper and lower estimates for the transition probability density of a Lévy process in $\rn$. Our approach relies on the complex analysis…
On the small-time behaviour of Lévy-type processes
V. Knopova, R. Schilling
We show some Chung-type law of the iterated logarithm results at zero for a class of (pure-jump) Feller or Lévy-type processes. This class includes all Lévy processes. Th…
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…
On the speed of convergence in the local limit theorem for triangular arrays of random variables
V. Knopova
We establish the upper bound on the speed of convergence to the infinitely divisible limit density in the local limit theorem for triangular arrays of random variables $\{X_{k,n},\…
Intrinsic small time estimates for distribution densities of Lévy processes
Victoria Knopova, Alexei Kulik
We construct intrinsic on-and off-diagonal upper and lower estimates for the transition probability density of a Lévy process in small time. By intrinsic we mean that such estimate…
Asymptotic behaviour of the distribution density of the fractional Lévy motion
Victoria Knopova, Alexei Kulik
We investigate the distribution properties of the fractional Lévy motion. We consider separately the cases (short memory) and (long memory), where is the Hu…
A note on the existence of transition probability densities for Lévy processes
V. Knopova, R. L. Schilling
We prove several necessary and sufficient conditions for the existence of (smooth) transition probability densities for Lévy processes and isotropic Lévy processes. Under some mild…
Exact asymptotic for distribution densities of Levy functionals
Victoria P. Knopova, Alexey M. Kulik
A version of the saddle point method is developed, which allows one to describe exactly the asymptotic behavior of distribution densities of Levy driven stochastic integrals with d…