上临界超过程的一类强极限的性质

Translated title of the contribution: On properties of a class of strong limits forsupercritical superprocesses

Yan Xia Ren, Renming Song, Rui Zhang

Research output: Contribution to journalArticlepeer-review

Abstract

Suppose that X = (Xt, t > 0; Pµ) is a supercritical superprocess in a locally compact separable metric space E. Let ϕ0 be a positive eigenfunction corresponding to the first eigenvalue λ0 of the generator of the mean semigroup of X. Then Mt := e−λ0t〈ϕ0, Xt〉 is a positive martingale. Let M∞ be the limit of Mt. It is known that M∞ is non-degenerate iff the Llog L condition is satisfied. When the Llog L condition may not be satisfied, Ren et al. (2017) recently proved that there exist a non-negative function γt on [0, ∞) and a non-degenerate random variable W such that for any finite nonzero Borel measure µ on E, limt→∞ γt〈ϕ0, Xt〉 = W, a.s.-Pµ. In this paper, we mainly investigate properties of W. We prove that W has strictly positive density on (0, ∞). We also investigate the small value and tail probability problems of W.

Translated title of the contributionOn properties of a class of strong limits forsupercritical superprocesses
Original languageChinese (Traditional)
Pages (from-to)485-504
Number of pages20
JournalScientia Sinica Mathematica
Volume49
Issue number3
DOIs
StatePublished - 2019

Keywords

  • absolute continuity
  • non-degenerate strong limit
  • small value probability
  • supercritical
  • superprocesses
  • tail probability

ASJC Scopus subject areas

  • General Mathematics

Fingerprint

Dive into the research topics of 'On properties of a class of strong limits forsupercritical superprocesses'. Together they form a unique fingerprint.

Cite this