68 citations · 159 across the 15 of their papers we have counts for
17 papers
Asymptotics of transition densities for Lévy processes with stochastic resetting
Kacper Budnik, Tomasz Grzywny, Paweł Sztonyk
We derive an explicit representation for the distribution of a Lévy process with total stochastic resetting and use it to investigate the asymptotic behaviour of the corresponding…
Decay of resolvent kernels and Schrödinger eigenstates for Lévy operators
Kamil Kaleta, René L. Schilling, Paweł Sztonyk
We study the spatial decay behaviour of resolvent kernels for a large class of non-local Lévy operators and bound states of the corresponding Schrödinger operators. Our findings na…
Nonlocal operators with Neumann conditions
Krzysztof Bogdan, Damian Fafuła, Paweł Sztonyk
We construct a strong Markov process corresponding to the Dirichlet form of Servadei and Valdinoci and use the process to solve the corresponding Neumann boundary problem for the f…
Heat kernels of non-local Schrödinger operators with Kato potentials
Tomasz Grzywny, Kamil Kaleta, Paweł Sztonyk
We study heat kernels of Schrödinger operators whose kinetic terms are non-local operators built for sufficiently regular symmetric Lévy measures with radial decreasing profiles an…
Strong Feller property for SDEs driven by multiplicative cylindrical stable noise
Tadeusz Kulczycki, Michał Ryznar, Paweł Sztonyk
We consider the stochastic differential equation , , driven by cylindrical -stable process in , where and .…
Spatial asymptotics at infinity for heat kernels of integro-differential operators
Kamil Kaleta, Paweł Sztonyk
We study a spatial asymptotic behaviour at infinity of kernels for convolution semigroups of nonlocal pseudo-differential operators. We give general and sharp sufficient c…