A Ray–Knight representation of up-down Chinese restaurants
نویسندگان
چکیده
We study composition-valued continuous-time Markov chains that appear naturally in the framework of Chinese Restaurant Processes (CRPs). As time evolves, new customers arrive (up-step) and existing leave (down-step) at suitable rates derived from ordered CRP Pitman Winkel (Ann. Probab. 37 (2009) 1999–2041). relate such up-down CRPs to splitting trees Lambert 38 (2010) 348–395) inducing spectrally positive Lévy processes. Conversely, we develop theorems Ray–Knight type recover more general heights processes with jumps marked by integer-valued paths. further establish limit for process paths connect work Forman, Pal, Rizzolo, Shi on interval partition diffusions hence some long-standing conjectures.
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ژورنال
عنوان ژورنال: Bernoulli
سال: 2022
ISSN: ['1573-9759', '1350-7265']
DOI: https://doi.org/10.3150/21-bej1364