scholarly journals Lévy processes: Concentration function and heat kernel bounds

Bernoulli ◽  
2020 ◽  
Vol 26 (4) ◽  
pp. 3191-3223
Author(s):  
Tomasz Grzywny ◽  
Karol Szczypkowski
Keyword(s):  
Heat Kernel ◽  
Lévy Processes ◽  
Levy Processes ◽  
Concentration Function ◽  
Kernel Bounds

scholarly journals Dirichlet heat kernel for unimodal Lévy processes

2014 ◽  
Vol 124 (11) ◽  
pp. 3612-3650 ◽  
Author(s):  
Krzysztof Bogdan ◽  
Tomasz Grzywny ◽  
Michał Ryznar
Keyword(s):  
Heat Kernel ◽  
Lévy Processes ◽  
Levy Processes ◽  
Dirichlet Heat Kernel

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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