8 citations · 22 across the 13 of their papers we have counts for
18 papers
Unifying Deep Stochastic Processes for Image Enhancement
Wojciech Kozłowski, Radosław Kuczbański, Kamil Adamczewski +2
Deep stochastic processes have recently become a central paradigm for image enhancement, with many methods explicitly conditioning the stochastic trajectory on the degraded input.…
Partial versus total resetting for Lévy flights in d dimensions: similarities and discrepancies
Costantino Di Bello, Aleksei Chechkin, Tomasz Grzywny +3
While stochastic resetting (or total resetting) is less young and more established concept in stochastic processes, partial stochastic resetting (PSR) is a relatively new field. PS…
Stationary states for stable processes with partial resetting
Tomasz Grzywny, Karol Szczypkowski, Zbigniew Palmowski +1
We study a -dimensional stochastic process which arises from a Lévy process by partial resetting, that is the position of the process at a…
Relativistic stable operators with critical potentials
Tomasz Jakubowski, Kamil Kaleta, Karol Szczypkowski
We give local in time sharp two sided estimates of the heat kernel associated with the relativistic stable operator perturbed by a critical (Hardy) potential.
Bound states and heat kernels for fractional-type Schrödinger operators with singular potentials
Tomasz Jakubowski, Kamil Kaleta, Karol Szczypkowski
We consider non-local Schrödinger operators in , , where the kinetic terms are pseudo-differential operators which are perturbations of th…
Non-symmetric Lévy-type operators
Jakub Minecki, Karol Szczypkowski
We present a general approach to the parametrix construction. We apply it to prove the uniqueness and existence of a weak fundamental solution for the equation $\partial_t =\mathca…
Sharp and plain estimates for Schrödinger perturbation of Gaussian kernel
Tomasz Jakubowski, Karol Szczypkowski
We investigate whether a fundamental solution of the Schrödinger equation has local in time sharp Gaussian estimates. We compare that class with the class…
Regularity of fundamental solutions for Lévy-type operators
Karol Szczypkowski
For a class of non-symmetric non-local Lévy-type operators , which include those of the form $$ \mathcal{L}^κf(x):= \int_{\mathbb{R}^d}( f(x+z)-f(x)- 1_{|z|<1} \left…
L{é}vy processes: concentration function and heat kernel bounds
Tomasz Grzywny, Karol Szczypkowski
We investigate densities of vaguely continuous convolution semigroups of probability measures on . We expose that many typical conditions on the characteristic expone…
Fundamental solution for super-critical non-symmetric Lévy-type operators
Karol Szczypkowski
We prove the existence and give estimates of the fundamental solution (the heat kernel) for the equation for non-symmetric non-local operators $$ \mathc…
Heat kernels of non-symmetric Lévy-type operators
Tomasz Grzywny, Karol Szczypkowski
We construct the fundamental solution (the heat kernel) to the equation , where under certain assumptions the operator takes one of…
Estimates of heat kernels of non-symmetric Lévy processes
Tomasz Grzywny, Karol Szczypkowski
We investigate densities of vaguely continuous convolution semigroups of probability measures on . First, we provide results that give upper estimates in a situation…
Sharp Gaussian estimates for heat kernels of Schrödinger operators
Krzysztof Bogdan, Jacek Dziubański, Karol Szczypkowski
We characterize functions for which the heat kernel of the Schrö\-dinger operator is comparable with the Gauss-Weierstrass kernel uniformly in space and time. In dim…
Characterization of sharp global Gaussian estimates for Schrödinger heat kernels
Krzysztof Bogdan, Jacek Dziubański, Karol Szczypkowski
We investigate when the fundamental solution of the Schrödinger equation posseses sharp Gaussian bounds global in space and time. We give a characterization for $V…
Sharp Gaussian estimates for Schrödinger heat kernels: integrability conditions
Krzysztof Bogdan, Jacek Dziubański, Karol Szczypkowski
We give new sufficient conditions for comparability of the fundamental solution of the Schrödinger equation with the Gauss-Weierstrass kernel and show that local $…
Kato classes for Lévy processes
Tomasz Grzywny, Karol Szczypkowski
We prove that the definitions of the Kato class by the semigroup and by the resolvent of the Lévy process on coincide if and only if 0 is not regular for {0}. If 0 i…
Gaussian estimates for Schroedinger perturbations
Krzysztof Bogdan, Karol Szczypkowski
We prove an optimal 4G Theorem for the Gaussian kernel. We also propose a new general method of estimating Schroedinger perturbations of transition densities, and give applications…
Estimates of gradient perturbation series
Tomasz Jakubowski, Karol Szczypkowski
We give upper and lower bounds of perturbation series for transition densities, corresponding to additive gradient perturbations satisfying certain space-time integrability conditi…