scholarly journals Gradient estimates of Dirichlet heat kernels for unimodal Lévy processes

2017 ◽  
Vol 291 (2-3) ◽  
pp. 374-397 ◽  
Author(s):  
Tadeusz Kulczycki ◽  
Michał Ryznar
Keyword(s):  
Lévy Processes ◽  
Levy Processes ◽  
Heat Kernels ◽  
Gradient Estimates

scholarly journals Coupling property and gradient estimates of Lévy processes via the symbol

Bernoulli ◽  
2012 ◽  
Vol 18 (4) ◽  
pp. 1128-1149 ◽  
Author(s):  
René L. Schilling ◽  
Paweł Sztonyk ◽  
Jian Wang
Keyword(s):  
Lévy Processes ◽  
Levy Processes ◽  
Gradient Estimates ◽  
Coupling Property

scholarly journals Estimates of heat kernels of non-symmetric Lévy processes

2021 ◽  
Vol 33 (5) ◽  
pp. 1207-1236
Author(s):  
Tomasz Grzywny ◽  
Karol Szczypkowski
Keyword(s):  
Lévy Processes ◽  
Characteristic Exponent ◽  
Levy Processes ◽  
Heat Kernels ◽  
Probability Measures ◽  
Convolution Semigroups

Abstract We investigate densities of vaguely continuous convolution semigroups of probability measures on ℝ d {{\mathbb{R}^{d}}} . First, we provide results that give upper estimates in a situation when the corresponding jump measure is allowed to be highly non-symmetric. Further, we prove upper estimates of the density and its derivatives if the jump measure compares with an isotropic unimodal measure and the characteristic exponent satisfies a certain scaling condition. Lower estimates are discussed in view of a recent development in that direction, and in such a way to complement upper estimates. We apply all those results to establish precise estimates of densities of non-symmetric Lévy processes.

On correlating Lévy processes

2010 ◽  
Vol 13 (1) ◽  
pp. 3-16 ◽  
Author(s):  
Ernst Eberlein ◽  
Dilip Madan
Keyword(s):  
Lévy Processes ◽  
Levy Processes

scholarly journals CLASSICAL MARKOV PROCESSES FROM QUANTUM LÉVY PROCESSES

1999 ◽  
Vol 02 (01) ◽  
pp. 105-129 ◽  
Author(s):  
UWE FRANZ
Keyword(s):  
Markov Process ◽  
Hopf Algebra ◽  
Markov Processes ◽  
Lévy Processes ◽  
Sufficient Conditions ◽  
Markov Property ◽  
Vacuum State ◽  
Levy Processes ◽  
Quantum Process ◽  
Quantum Markov Processes

We show how classical Markov processes can be obtained from quantum Lévy processes. It is shown that quantum Lévy processes are quantum Markov processes, and sufficient conditions for restrictions to subalgebras to remain quantum Markov processes are given. A classical Markov process (which has the same time-ordered moments as the quantum process in the vacuum state) exists whenever we can restrict to a commutative subalgebra without losing the quantum Markov property.8 Several examples, including the Azéma martingale, with explicit calculations are presented. In particular, the action of the generator of the classical Markov processes on polynomials or their moments are calculated using Hopf algebra duality.

Sign in / Sign up

Export Citation Format

Share Document