Gradient estimates of harmonic functions and transition densities for Lévy processes
T Kulczycki, M Ryznar - Transactions of the American Mathematical Society, 2016 - ams.org
We prove gradient estimates for harmonic functions with respect to a $ d $-dimensional
unimodal pure-jump Lévy process under some mild assumptions on the density of its Lévy …
unimodal pure-jump Lévy process under some mild assumptions on the density of its Lévy …
Strong convergence of the Euler–Maruyama approximation for a class of Lévy-driven SDEs
F Kühn, RL Schilling - Stochastic Processes and their Applications, 2019 - Elsevier
Consider the following stochastic differential equation (SDE) d X t= b (t, X t−) d t+ d L t, X 0=
x, driven by a d-dimensional Lévy process (L t) t≥ 0. We establish conditions on the Lévy …
x, driven by a d-dimensional Lévy process (L t) t≥ 0. We establish conditions on the Lévy …
Existence of densities for stable-like driven SDEʼs with Hölder continuous coefficients
A Debussche, N Fournier - Journal of functional analysis, 2013 - Elsevier
Consider a multidimensional stochastic differential equation driven by a stable-like Lévy
process. We prove that the law of the solution immediately has a density in some Besov …
process. We prove that the law of the solution immediately has a density in some Besov …
[HTML][HTML] Estimates of transition densities and their derivatives for jump Lévy processes
Estimates of transition densities and their derivatives for jump Lévy processes - ScienceDirect
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Estimates of heat kernels of non-symmetric Lévy processes
T Grzywny, K Szczypkowski - Forum Mathematicum, 2021 - degruyter.com
We investigate densities of vaguely continuous convolution semigroups of probability
measures on ℝ d. First, we provide results that give upper estimates in a situation when the …
measures on ℝ d. First, we provide results that give upper estimates in a situation when the …
Strong rate of convergence of the Euler scheme for SDEs with irregular drift driven by Levy noise
We study the strong rate of convergence of the Euler--Maruyama scheme for a
multidimensional stochastic differential equation (SDE) $$ dX_t= b (X_t) dt+ dL_t, $$ with …
multidimensional stochastic differential equation (SDE) $$ dX_t= b (X_t) dt+ dL_t, $$ with …
[HTML][HTML] Coupling and exponential ergodicity for stochastic differential equations driven by Lévy processes
MB Majka - Stochastic processes and their applications, 2017 - Elsevier
We present a novel idea for a coupling of solutions of stochastic differential equations driven
by Lévy noise, inspired by some results from the optimal transportation theory. Then we use …
by Lévy noise, inspired by some results from the optimal transportation theory. Then we use …
Heat kernel of anisotropic nonlocal operators
Heat Kernel of Anisotropic Nonlocal Operators Page 1 Documenta Math. 1 Heat Kernel of
Anisotropic Nonlocal Operators Krzysztof Bogdan, Pawe l Sztonyk, and Victoria Knopova …
Anisotropic Nonlocal Operators Krzysztof Bogdan, Pawe l Sztonyk, and Victoria Knopova …
Davie's type uniqueness for a class of SDEs with jumps
E Priola - 2018 - projecteuclid.org
A result of AM Davie (Int. Math. Res. Not. 24 (2007) rnm124) states that a multidimensional
stochastic equation dX_t=b(t,X_t)\,dt+dW_t, X_0=x, driven by a Wiener process W=(W_t) with …
stochastic equation dX_t=b(t,X_t)\,dt+dW_t, X_0=x, driven by a Wiener process W=(W_t) with …
-Wasserstein distance for stochastic differential equations driven by Lévy processes
J Wang - 2016 - projecteuclid.org
Coupling by reflection mixed with synchronous coupling is constructed for a class of
stochastic differential equations (SDEs) driven by Lévy noises. As an application, we …
stochastic differential equations (SDEs) driven by Lévy noises. As an application, we …