Previous work constructed Fleming–Viot-type measure-valued diffusions (and diffusions on a space of interval partitions of the unit interval [0,1]) that are stationary with respect to the Poisson–Dirichlet random measures with parameters \alpha \in (0,1) and \theta > -\alpha. In this paper, we complete the proof that these processes resolve a conjecture by Feng and Sun [Probab. Theory Related Fields 148 (2010), pp. 501–525] by showing that the processes of ranked atom sizes (or of ranked interval lengths) of these diffusions are members of a two-parameter family of diffusions introduced by Petrov [Funct. Anal. Appl. 43 (2009), pp. 279–296], extending a model by Ethier and Kurtz [Adv. in Appl. Probab. 13 (1981), pp. 429–452] in the case \alpha =0.
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Functional central limit theorem via nonstationary projective conditions
In this paper we survey some recent progress on the Gaussian approximation for
nonstationary dependent structures via martingale methods. First we present general
theorems involving projective conditions for triangular arrays of random variables and
then present various applications for rho-mixing and alpha-dependent triangular arrays,
stationary sequences in a random time scenery, application to the quenched FCLT, application
to linear statistics with alpha-dependent innovations, application to functions
of a triangular stationary Markov chain.
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- Award ID(s):
- 2054598
- PAR ID:
- 10415128
- Editor(s):
- Radosław Adamczak, Nathael Gozlan
- Date Published:
- Journal Name:
- Progress in probability
- ISSN:
- 1050-6977
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
