Continuity of eigenvalues of subordinate processes in domains

Zhen Qing Chen, Renming Song

Research output: Contribution to journalArticlepeer-review

Abstract

Let X = {Xt, t ≥ 0} be a symmetric Markov process in a state space E and D an open set of E. Let S(n) = {St( n), t ≥ 0} be a subordinator with Laplace exponent φn and S = {St, t ≥ 0} a subordinator with Laplace exponent φ. Suppose that X is independent of S and S ( n ). In this paper we consider the subordinate processes [InlineMediaObject not available: see fulltext.] and [InlineMediaObject not available: see fulltext.] and their subprocesses [InlineMediaObject not available: see fulltext.] and Xφn, D killed upon leaving D. Suppose that the spectra of the semigroups of [InlineMediaObject not available: see fulltext.] and Xφ, D are all discrete, with [InlineMediaObject not available: see fulltext.] being the eigenvalues of the generator of [InlineMediaObject not available: see fulltext.] and [InlineMediaObject not available: see fulltext.] being the eigenvalues of the generator of Xφ, D. We show that, if lim n →∞ φn (λ)=φ (λ) for every λ>0, then [InlineMediaObject not available: see fulltext.].

Original languageEnglish (US)
Pages (from-to)71-89
Number of pages19
JournalMathematische Zeitschrift
Volume252
Issue number1
DOIs
StatePublished - Jan 1 2006

ASJC Scopus subject areas

  • Mathematics(all)

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