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Abstract: A fragmentation of a set $A$ is a graph with vertices labeled by subsets of $A$ which obey a certain parent-child relationship. A random fragmentation tree is a probability distribution on t...
Abstract: Starting from the forward and backward infinitesimal generators of bilateral, time-homogeneous Markov processes, the self-adjoint Hamiltonians of the generalized Schroedinger equations are f...
We prove the existence of a local time, the continuity of the local time about t, and the regular property for a.e. x ∈ R of a Ornstein-Uhlenbeck type {Xt, t ∈ R+} driven by a general L´evy proc...
We prove the metastable behavior of reversible Markov processes on finite state spaces under minimal conditions on the jump rates. To illustrate the result we deduce the metastable behavior of the Isi...
The study of multidimensional stochastic processes involves complex computations in intricate functional spaces. In particular, the diffusion processes, which include the practically important Gauss-M...
We construct a four-parameter family of Markov processes on infinite Gelfand-Tsetlin schemes that preserve the class of central (Gibbs) measures. Any process in the family induces a Feller Markov proc...
Transience and recurrence are among the most important concepts in Markov processes. In this paper, we study the transience and recurrence for right processes with a given weight function, and charact...

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