Inverting Ray-Knight identity

Ray-knight Theorems via Continuous Trees

In this paper, we are interested in obtaining the generalized Ray-Knight theorems (previously proved by Yor 10]) using branching processes. It was already observed in O'Connell's thesis 6] that the construction of the natural tree associated to Brownian excursion (Le Gall 4], Neveu-Pitman 5]) enables to obtain one of the "classical" Ray-Knight theorems. Our aim is to use the same ideas to get t...

Lecture 1: Generalized Ray Knight Theorem for Finite Markov Chains

A direct proof of the Ray-Knight theorem

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Binary trees, exploration processes, and an extented Ray–Knight Theorem

We study the bijection betwen binary Galton Watson trees in continuous time and their exploration process, both in the suband in the supercritical cases. We then take the limit over renormalized quantities, as the size of the population tends to infinity. We thus deduce Delmas’ generalization of the second Ray–Knight theorem.

Branching processes with competition and generalized Ray Knight Theorem

We consider a discrete model of population with interaction where the birth and death rates are non linear functions of the population size. After proceeding to renormalization of the model parameters, we obtain in the limit of large population that the population size evolves as a diffusion solution of the SDE