On the Existence and Explicit Estimates for the Coupling Property of Lévy Processes with Drift

2012 ◽  
Vol 27 (3) ◽  
pp. 1021-1044 ◽  
Author(s):  
Jian Wang
Keyword(s):  
Lévy Processes ◽  
Levy Processes ◽  
Coupling Property

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

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.

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