HEAT KERNEL ESTIMATES FOR SYMMETRIC JUMP PROCESSES WITH MIXED POLYNOMIAL GROWTHS

Bae J, Kang J, Kim P, Lee J (2019)
ANNALS OF PROBABILITY 47(5): 2830-2868.

Zeitschriftenaufsatz | Veröffentlicht| Englisch
 
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Autor/in
Bae, Joohak; Kang, JaehoonUniBi; Kim, Panki; Lee, Jaehun
Abstract / Bemerkung
In this paper, we study the transition densities of pure-jump symmetric Markov processes in R-d, whose jumping kernels are comparable to radially symmetric functions with mixed polynomial growths. Under some mild assumptions on their scale functions, we establish sharp two-sided estimates of the transition densities (heat kernel estimates) for such processes. This is the first study on global heat kernel estimates of jump processes (including non-Levy processes) whose weak scaling index is not necessarily strictly less than 2. As an application, we proved that the finite second moment condition on such symmetric Markov process is equivalent to the Khintchine-type law of iterated logarithm at infinity.
Stichworte
Dirichlet form; symmetric Markov process; transition density; heat; kernel estimates; law of iterated logarithm
Erscheinungsjahr
2019
Zeitschriftentitel
ANNALS OF PROBABILITY
Band
47
Ausgabe
5
Seite(n)
2830-2868
ISSN
0091-1798
Page URI
https://pub.uni-bielefeld.de/record/2938755

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Bae J, Kang J, Kim P, Lee J. HEAT KERNEL ESTIMATES FOR SYMMETRIC JUMP PROCESSES WITH MIXED POLYNOMIAL GROWTHS. ANNALS OF PROBABILITY. 2019;47(5):2830-2868.
Bae, J., Kang, J., Kim, P., & Lee, J. (2019). HEAT KERNEL ESTIMATES FOR SYMMETRIC JUMP PROCESSES WITH MIXED POLYNOMIAL GROWTHS. ANNALS OF PROBABILITY, 47(5), 2830-2868. doi:10.1214/18-AOP1323
Bae, J., Kang, J., Kim, P., and Lee, J. (2019). HEAT KERNEL ESTIMATES FOR SYMMETRIC JUMP PROCESSES WITH MIXED POLYNOMIAL GROWTHS. ANNALS OF PROBABILITY 47, 2830-2868.
Bae, J., et al., 2019. HEAT KERNEL ESTIMATES FOR SYMMETRIC JUMP PROCESSES WITH MIXED POLYNOMIAL GROWTHS. ANNALS OF PROBABILITY, 47(5), p 2830-2868.
J. Bae, et al., “HEAT KERNEL ESTIMATES FOR SYMMETRIC JUMP PROCESSES WITH MIXED POLYNOMIAL GROWTHS”, ANNALS OF PROBABILITY, vol. 47, 2019, pp. 2830-2868.
Bae, J., Kang, J., Kim, P., Lee, J.: HEAT KERNEL ESTIMATES FOR SYMMETRIC JUMP PROCESSES WITH MIXED POLYNOMIAL GROWTHS. ANNALS OF PROBABILITY. 47, 2830-2868 (2019).
Bae, Joohak, Kang, Jaehoon, Kim, Panki, and Lee, Jaehun. “HEAT KERNEL ESTIMATES FOR SYMMETRIC JUMP PROCESSES WITH MIXED POLYNOMIAL GROWTHS”. ANNALS OF PROBABILITY 47.5 (2019): 2830-2868.