PERIODIC HOMOGENIZATION OF NONSYMMETRIC LÉVY-TYPE PROCESSES

Xin Chen*, Zhen Qing Chen, Takashi Kumagai, Jian Wang

*この研究の対応する著者

研究成果: Article査読

1 被引用数 (Scopus)

抄録

In this paper we study homogenization problem for strong Markov processes on ℝd having infinitesimal gener (formula presented) in periodic media, where Π is a nonnegative measure on d that does not charge the origin 0, satisfies (formula presented) and can be singular with respect to the Lebesgue measure on ℝd. Under a proper scaling we show the scaled processes converge weakly to Lévy processes on ℝd. The results are a counterpart of the celebrated work (Asymptotic Analysis for Periodic Structures (1978) North-Holland; Ann. Probab. 13 (1985) 385–396) in the jump-diffusion setting. In particular, we completely characterize the homogenized limiting processes when b(x) is a bounded continuous multivariate 1-periodic ℝd -valued function, k(x,z) is a nonnegative bounded continuous function that is multivariate 1-periodic in both x and z variables and, in spherical coordinate (formula presented) (formula presented) with (formula presented) and e0 being any finite measure on the unit sphere (formula presented) in Rd. Different phenomena occur depending on the values of α; there are five cases: α ∈(0, 1), α = 1, α ∈ (1, 2), α = 2 and α ∈ (2,∞).

本文言語English
ページ(範囲)2874-2921
ページ数48
ジャーナルAnnals of Probability
49
6
DOI
出版ステータスPublished - 2021
外部発表はい

ASJC Scopus subject areas

  • 統計学および確率
  • 統計学、確率および不確実性

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