Naslov
Periodic homogenisation of a Lévy-type process with small jumps

Autori
Sandrić, Nikola ; Valentić, Ivana ; Wang, Jian

Izvornik
Journal of evolution equations (1424-3199) 21 (2021), 1; 771-803

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Feller process, homogenization, Lévy-type process, pseudo-differential operator, semimartingale characteristics

Sažetak
In this article, we consider the problem of periodic homogenization of a Feller process generated by a pseudo-differential operator, the so- called Lévy-type process. Under the assumptions that the generator has rapidly periodically oscillating coefficients, and that it admits “small jumps” only (that is, the jump kernel has finite second moment), we prove that the appropriately centered and scaled process converges weakly to a Brownian motion with covariance matrix given in terms of the coefficients of the generator. The presented results generalize the classical and well-known results related to periodic homogenization of a diffusion process.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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