40 citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- National Academy of Sciences of UkraineUA6 papers
- Institute of MathematicsPL3 papers
- National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”UA3 papers
- Mathematical Institute of the Slovak Academy of SciencesSK2 papers
- Taras Shevchenko National University of KyivUA2 papers
- Frantsevich Institute for Problems in Materials ScienceUA1 paper
- Institute for Information RecordingUA1 paper
- Iowa State UniversityUS1 paper
- National Academy of Medical Sciences of UkraineUA1 paper
- National Academy of SciencesUS1 paper
- Technische Universität DresdenDE1 paper
- University of Colorado BoulderUS1 paper
9 papers · 1 filter
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 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…
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…
The Bernoulli sieve: an overview
Alexander Gnedin, Alexander Iksanov, Alexander Marynych
The Bernoulli sieve is a version of the classical balls-in-boxes occupancy scheme, in which random frequencies of infinitely many boxes are produced by a multiplicative random walk…
Transition density estimates for a class of Lévy and Lévy-type processes
V. Knopova, R. Schilling
We show on- and off-diagonal upper estimates for the transition densities of symmetric Levy and Levy-type processes. To get the an-diagonal estimates we prove a Nash type inequalit…
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…
Small parts in the Bernoulli sieve
Alexander Gnedin, Alex Iksanov, Uwe Roesler
Sampling from a random discrete distribution induced by a `stick-breaking' process is considered. Under a moment condition, it is shown that the asymptotics of the sequence of occu…