scholarly journals Intertwining, excursion theory and Krein theory of strings for non-self-adjoint Markov semigroups

2019 ◽  
Vol 47 (5) ◽  
pp. 3231-3277 ◽  
Author(s):  
Pierre Patie ◽  
Mladen Savov ◽  
Yixuan Zhao
Keyword(s):  
Markov Semigroups ◽  
Excursion Theory

Group Transference Techniques for the Estimation of the Decoherence Times and Capacities of Quantum Markov Semigroups

2021 ◽  
Vol 67 (5) ◽  
pp. 2878-2909
Author(s):  
Ivan Bardet ◽  
Marius Junge ◽  
Nicholas Laracuente ◽  
Cambyse Rouze ◽  
Daniel Stilck Franca
Keyword(s):  
Markov Semigroups

scholarly journals RIESZ TRANSFORMS ON COMPACT QUANTUM GROUPS AND STRONG SOLIDITY

2021 ◽  
pp. 1-37
Author(s):  
Martijn Caspers
Keyword(s):  
Quantum Group ◽  
Quantum Groups ◽  
Riesz Transform ◽  
Wreath Products ◽  
Compact Quantum Group ◽  
Riesz Transforms ◽  
Markov Semigroup ◽  
Markov Semigroups ◽  
Free Products ◽  
Compact Quantum Groups

Abstract One of the main aims of this paper is to give a large class of strongly solid compact quantum groups. We do this by using quantum Markov semigroups and noncommutative Riesz transforms. We introduce a property for quantum Markov semigroups of central multipliers on a compact quantum group which we shall call ‘approximate linearity with almost commuting intertwiners’. We show that this property is stable under free products, monoidal equivalence, free wreath products and dual quantum subgroups. Examples include in particular all the (higher-dimensional) free orthogonal easy quantum groups. We then show that a compact quantum group with a quantum Markov semigroup that is approximately linear with almost commuting intertwiners satisfies the immediately gradient- ${\mathcal {S}}_2$ condition from [10] and derive strong solidity results (following [10]). Using the noncommutative Riesz transform we also show that these quantum groups have the Akemann–Ostrand property; in particular, the same strong solidity results follow again (now following [27]).

Correlation and Brascamp-Lieb Inequalities for Markov Semigroups

2010 ◽  
Author(s):  
F. Barthe ◽  
D. Cordero-Erausquin ◽  
M. Ledoux ◽  
B. Maurey
Keyword(s):  
Markov Semigroups

scholarly journals Gerber–Shiu distribution at Parisian ruin for Lévy insurance risk processes

2016 ◽  
Vol 53 (2) ◽  
pp. 572-584 ◽  
Author(s):  
Erik J. Baurdoux ◽  
Juan Carlos Pardo ◽  
José Luis Pérez ◽  
Jean-François Renaud
Keyword(s):  
Risk Process ◽  
Levy Processes ◽  
Insurance Company ◽  
Excursion Theory ◽  
Insurance Risk ◽  
Scale Functions ◽  
Surplus Process ◽  
Parisian Ruin ◽  
Risk Processes ◽  
Spectrally Negative Lévy Processes

Abstract Inspired by the works of Landriault et al. (2011), (2014), we study the Gerber–Shiu distribution at Parisian ruin with exponential implementation delays for a spectrally negative Lévy insurance risk process. To be more specific, we study the so-called Gerber–Shiu distribution for a ruin model where at each time the surplus process goes negative, an independent exponential clock is started. If the clock rings before the surplus becomes positive again then the insurance company is ruined. Our methodology uses excursion theory for spectrally negative Lévy processes and relies on the theory of so-called scale functions. In particular, we extend the recent results of Landriault et al. (2011), (2014).

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