Inverting Ray-Knight identity

Sabot, Christophe; Tarres, Pierre

Sabot, Christophe; Tarres, Pierre (2016), Inverting Ray-Knight identity, Probability Theory and Related Fields, 165, 3, p. 559-580. 10.1007/s00440-015-0640-x

Type

Article accepté pour publication ou publié

External document link

https://arxiv.org/abs/1311.6622v2

Date

2016

Journal name

Probability Theory and Related Fields

Volume

165

Number

Publisher

Springer

Pages

559-580

Abstract (EN)

We provide a short proof of the Ray-Knight second generalized Theorem, using a martingale which can be seen (on the positive quadrant) as the Radon–Nikodym derivative of the reversed vertex-reinforced jump process measure with respect to the Markov jump process with the same conductances. Next we show that a variant of this process provides an inversion of that Ray-Knight identity. We give a similar result for the Ray-Knight first generalized Theorem.

Subjects / Keywords

Ray-Knight identity; martingale; Markov jump process; Gaussian free field

JEL

C11 - Bayesian Analysis: General