α-CONTINUITY PROPERTIES OF THE SYMMETRIC α-STABLE PROCESS

α-CONTINUITY PROPERTIES OF THE SYMMETRIC α-STABLE PROCESS (2004)

by R. Dante , Deblassie , Pedro J. M Éndez-hernández

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Datum	Value	Source
TITLE	α-CONTINUITY PROPERTIES OF THE SYMMETRIC α-STABLE PROCESS	SVM HeaderParse 0.2
AUTHOR NAME	R. Dante	SVM HeaderParse 0.2
AUTHOR NAME	Deblassie	SVM HeaderParse 0.2
AUTHOR NAME	Pedro J. M Éndez-hernández	SVM HeaderParse 0.2
ABSTRACT	Abstract. Let D be a domain of finite Lebesgue measure in Rd and let XD t be the symmetric α-stable process killed upon exiting D. Each element of the set {λα i}∞i=1 of eigenvalues associated to XD t, regarded as a function of α ∈ (0, 2), is right continuous. In addition, if D is Lipschitz and bounded, then each λα i is continuous in α and the set of associated eigenfunctions is precompact. We also prove that if D is a domain of finite Lebesgue measure, then for all 0 < α < β ≤ 2 and i ≥ 1, λ α i ≤ λ β] α/β i Previously, this bound had been known only for β = 2 and α rational. 1.	SVM HeaderParse 0.2
YEAR	2004	SVM HeaderParse 0.2
CITATIONS	19 found	ParsCit 1.0