T. Kulczycki

activity

20042026

α

-harmonic functions

99 citations · 217 across the 27 of their papers we have counts for

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18 papers · 1 filter

math.PR2024

Intrinsic ultracontractivity for Schrödinger semigroups based on cylindrical fractional Laplacian on the plane

Tadeusz Kulczycki, Kinga Sztonyk

We study Schrödinger operators on $R^{2}$ $H = (- \frac{\partial ^{2}}{\partial x _{1}^{2}})^{α /2} + (- \frac{\partial ^{2}}{\partial x _{2}^{2}})^{α /2} + V,$ for $α…

math.PR2022

Drift reduction method for SDEs driven by inhomogeneous singular L{é}vy noise

Tadeusz Kulczycki, Oleksii Kulyk, Michał Ryznar

We study SDE $d X_{t} = b (X_{t}) d t + A (X_{t -}) d Z_{t}, X_{0} = x \in R^{d}, t \geq 0$ where $Z = (Z^{1}, \dots, Z^{d})^{T}$ , with $Z^{i}, i = 1, \dots, d$ being indepen…

math.PR2021★ 1 cited

On weak solution of SDE driven by inhomogeneous singular Lévy noise

Tadeusz Kulczycki, Alexei Kulik, Michał Ryznar

We study a time-inhomogeneous SDE in $R^{d}$ driven by a cylindrical Lévy process with independent coordinates which may have different scaling properties. Such a structure of the d…

math.PR2019★ 2 cited

Semigroup properties of solutions of SDEs driven by L{é}vy processes with independent coordinates

Tadeusz Kulczycki, Michal Ryznar

We study the stochastic differential equation $d X_{t} = A (X_{t -}) d Z_{t}$ , $X_{0} = x$ , where $Z_{t} = (Z_{t}^{(1)}, \dots, Z_{t}^{(d)})^{T}$ and $Z_{t}^{(1)}, \dots, Z_{t}^{(d)}$ are independen…

math.PR2018

Strong Feller property for SDEs driven by multiplicative cylindrical stable noise

Tadeusz Kulczycki, Michał Ryznar, Paweł Sztonyk

We consider the stochastic differential equation $d X_{t} = A (X_{t -}) d Z_{t}$ , $X_{0} = x$ , driven by cylindrical $α$ -stable process $Z_{t}$ in $R^{d}$ , where $α \in (0, 1)$ and $d \geq 2$ .…

math.PR2017

Transition density estimates for diagonal systems of SDEs driven by cylindrical $α$ -stable processes