Heat kernel estimates for subordinate Brownian motions
By Ante Mimica. 2015
54 citations recorded by the source corpus.
In this article, we study transition probabilities of a class of subordinate Brownian motions. Under mild assumptions on the Laplace exponent of the corresponding subordinator, sharp two‐sided estimates of the transition probability are established. This approach, in particular, covers subordinators with Laplace exponents that vary regularly at infinity with index one, for example, ϕ(λ)=λlog(1+λ)-1orϕ(λ)=λlog(1+λβ/2),β∈(0,2) that correspond to subordinate Brownian motions with scaling order that is not necessarily strictly between 0 and 2. These estimates are applied to estimate Green function (potential) of subordinate Brownian motion. We also prove the equivalence of the lower scaling condition of the Laplace exponent and the near diagonal upper estimate of the transition estimate.
Subfields: Finance, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/2aea4cf1c3258ef58082a41ae51eae71a025e0d9
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In Mathematical Physics
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Citations in the corpus
- Mixed local and nonlocal elliptic operators: regularity and maximum principles (2020, background): “6 in [41]), regularization effects of Cahn-Hilliard equations (see [18]), numerics ([12]), probability and stochastics (see [19, 20, 42]), symmetry results for mixed range phase transitions (see [16]), porous medium equations (see [24]), decay estimates for parabolic equations (see [31]), specific L”