Heat kernel estimates for subordinate Brownian motions (CROSBI ID 231759)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Mimica, Ante
engleski
Heat kernel estimates for subordinate Brownian motions
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, $$ \phi(\lambda)=\frac{; ; ; ; ; \lambda}; ; ; ; ; {; ; ; ; ; \log(1+\lambda)}; ; ; ; ; -1 \text{; ; ; ; ; or }; ; ; ; ; \phi(\lambda)=\frac{; ; ; ; ; \lambda}; ; ; ; ; {; ; ; ; ; \log(1+\lambda^{; ; ; ; ; \beta/2}; ; ; ; ; )}; ; ; ; ; , \beta\in (0, 2) $$ 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.
heat kernel estimates ; Laplace exponent ; Levy measure ; subordinator ; subordinate Brownian motion
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Podaci o izdanju
113 (3)
2016.
627-648
objavljeno
0024-6115
1460-244X
10.1112/plms/pdw043