A robust spectral method for finding lumpings and meta stable states of non-reversible Markov chains.
A scaling result for explosive processes.
A second order SDE for the Langevin process reflected at a completely inelastic boundary
It was shown in [2] that a Langevin process can be reflected at an energy absorbing boundary. Here, we establish that the law of this reflecting process can be characterized as the unique weak solution to a certain second order stochastic differential equation with constraints, which is in sharp contrast with a deterministic analog.
A semigroup charaterization of the multiparameter Wiener process.
A semi-markovian model for the brownian motion
A short proof of the Hausdorff dimension formula for Lévy processes.
A simple approach to functional inequalities for non-local Dirichlet forms
With direct and simple proofs, we establish Poincaré type inequalities (including Poincaré inequalities, weak Poincaré inequalities and super Poincaré inequalities), entropy inequalities and Beckner-type inequalities for non-local Dirichlet forms. The proofs are efficient for non-local Dirichlet forms with general jump kernel, and also work for Lp(p> 1) settings. Our results yield a new sufficient condition for fractional Poincaré inequalities, which were recently studied in [P.T. Gressman,...
A simple interpretation of two stochastic processes subject to an independent death process.
A simple proof of a theorem on Markov operators
A simple proof of Doob's convergence theorem
A simple proof of the continuity of the higher order Riesz transforms with respect to the gaussian measure
A simple proof of the logarithmic Sobolev inequality on the circle
A simple proof of the Poincaré inequality for a large class of probability measures.
A simple proof of the support theorem for diffusion processes
A simplified proof of the Sevastyanov theorem on branching processes
A stability theorem for elliptic Harnack inequalities
We prove a stability theorem for the elliptic Harnack inequality: if two weighted graphs are equivalent, then the elliptic Harnack inequality holds for harmonic functions with respect to one of the graphs if and only if it holds for harmonic functions with respect to the other graph. As part of the proof, we give a characterization of the elliptic Harnack inequality.
A stochastic cobweb dynamical model.
A stochastic death pairing process.
A stochastic extension of R. Thomas regulatory network modelling
In this paper we present the extension of the kinetic logic proposed by René Thomas for analysis of genetic regulatory gene networks. We consider the case with a Gaussian noise added to the regulation function and propose a method of analyzing the resulting model with a discrete time Markov model.
A stochastic fixed point equation for weighted minima and maxima
Given any finite or countable collection of real numbers Tj, j∈J, we find all solutions Fto the stochastic fixed point equation whereW and the Wj, j∈J, are independent real-valued random variables with distribution Fand means equality in distribution. The bulk of the necessary analysis is spent on the case when |J|≥2 and all Tj are (strictly) positive. Nontrivial solutions are then concentrated on either the positive or negative half line. In the most interesting (and difficult) situation T...