Convergence Analysis of the Spectral Expansion of Stable Related Semigroups

Yixuan Zhao () and Pierre Patie ()
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Yixuan Zhao: Cornell University, Cornell University ORIE Department
Pierre Patie: Cornell University, Cornell University ORIE Department

A chapter in Mathematical and Computational Approaches in Advancing Modern Science and Engineering, 2016, pp 787-797 from Springer

Abstract: Abstract The purpose of this note is to carry out a convergence analysis of the spectral representation, derived recently in Patie and Savov (Spectral expansions of non-self-adjoint generalized Laguerre semigroups, submitted, 2015), of some non-self-adjoint Markovian semigroups related to spectrally negative α-stable Lévy processes conditioned to stay positive. More specifically, we start by performing an error analysis for the spectral type series expansions. Moreover, these semigroups are closely related to a class of invariant semigroups, whose speed of convergence to equilibrium has been studied in Patie and Savov (Spectral expansions of non-self-adjoint generalized Laguerre semigroups, submitted, 2015). Our second aim is to carry out a numerical analysis on the convergence rate which is illustrated with two examples.

Keywords: Markov Semigroup; Spectral Expansion; Convolution Semigroup; Fell Semigroup; Unique Invariant Measure (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-30379-6_70

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DOI: 10.1007/978-3-319-30379-6_70

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