Spectral decomposition of fractional operators and a reflected stable semigroup

DOI10.1016/j.jde.2016.10.026zbMath1368.47032arXiv1606.04034OpenAlexW2963063348MaRDI QIDQ729923

Pierre Patie, Yixuan Zhao

Publication date: 22 December 2016

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.04034

zbMATH Keywords

spectral theoryMarkov semigroupsfractional operatorscontinuous framesnon-self-adjoint integro-differential operatorsreflected stable processes

Mathematics Subject Classification ID

Markov semigroups and applications to diffusion processes (47D07) General harmonic expansions, frames (42C15) Stable stochastic processes (60G52) Spectral theory; eigenvalue problems on manifolds (58C40) Integro-differential operators (47G20) Fractional partial differential equations (35R11)

Related Items (11)

Fluctuation theory for Lévy processes with completely monotone jumps ⋮ Bernstein-gamma functions and exponential functionals of Lévy processes ⋮ Option Pricing in a One-Dimensional Affine Term Structure Model via Spectral Representations ⋮ Fractional partial differential equations with boundary conditions ⋮ Smoothness of continuous state branching with immigration semigroups ⋮ Risk‐neutral pricing techniques and examples ⋮ Weak similarity orbit of (log)‐self‐similar Markov semigroups on the Euclidean space ⋮ On interweaving relations ⋮ Intertwining, excursion theory and Krein theory of strings for non-self-adjoint Markov semigroups ⋮ Self-similar Cauchy problems and generalized Mittag-Leffler functions ⋮ Analysis of non-reversible Markov chains via similarity orbits

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On \(L^{p}\)-contractivity of Laguerre semigroups
• Intertwining certain fractional derivatives
• Predicting the ultimate supremum of a stable Lévy process with no negative jumps
• Infinite divisibility of solutions to some self-similar integro-differential equations and exponential functionals of Lévy processes
• Jensen polynomials and the Turán and Laguerre inequalities
• Exponentially small expansions in the asymptotics of the Wright function
• Infinitesimal generators of time changed processes
• An extension of Pitman's theorem for spectrally positive Lévy processes
• Cauchy problem of the non-self-adjoint Gauss-Laguerre semigroups and uniform bounds for generalized Laguerre polynomials
• Introductory lectures on fluctuations of Lévy processes with applications.
• An introduction to infinite-dimensional analysis
• Recurrent extensions of self-similar Markov processes and Cramér's condition
• Frames and semi-frames
• Elementary Solutions for Certain Parabolic Partial Differential Equations
• Reflected spectrally negative stable processes and their governing equations
• Some results on non-self-adjoint operators, a survey
• On construction of Markov processes
• On Entire Moments of Self-Similar Markov Processes
• Semi-stable Markov processes. I
• Variational formulation for the stationary fractional advection dispersion equation
• Classical Expansions and Their Relation to Conjugate Harmonic Functions
• Markov processes and their functional in duality
• Mesures Associees Aux Fonctionnelles Additives de Markov. I
• Markov Processes, Brownian Motion, and Time Symmetry
• AN EXAMPLE IN THE THEORY OF THE SPECTRUM OF A FUNCTION
• Stochastic models for fractional calculus
• Bernstein functions. Theory and applications

This page was built for publication: Spectral decomposition of fractional operators and a reflected stable semigroup