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Small time asymptotics of spectral heat contents for subordinate killed Brownian motions related to isotropic α ‐stable processes
Author(s) -
Park Hyunchul,
Song Renming
Publication year - 2019
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms.12235
Subject(s) - subordinator , mathematics , brownian motion , isotropy , bounded function , mathematical analysis , heat equation , domain (mathematical analysis) , asymptotic expansion , heat kernel , term (time) , mathematical physics , pure mathematics , physics , statistics , quantum mechanics
In this paper, we study the small time asymptotic behavior of the spectral heat contentQ ∼ D ( α )( t )of an arbitrary bounded C 1 , 1domain D with respect to the subordinate killed Brownian motion in D via an ( α / 2 ) ‐stable subordinator. For all α ∈ ( 0 , 2 ) , we establish a two‐term small time expansion forQ ∼ D ( α )( t )in all dimensions. When α ∈ ( 1 , 2 ) and d ⩾ 2 , we establish a three‐term small time expansion forQ ∼ D ( α )( t ) .