The "local" law of the iterated logarithm for processes related to Lévy's stochastic area process
The logarithmic Sobolev constant of some finite Markov chains
The logarithmic Sobolev constant is always bounded above by half the spectral gap. It is natural to ask when this inequality is an equality. We consider this question in the context of reversible Markov chains on small finite state spaces. In particular, we prove that equality holds for simple random walk on the five cycle and we discuss assorted families of chains on three and four points.
The -Wright function in time-fractional diffusion processes: a tutorial survey.
The Markov chain asymptotics of random mapping graphs
The Markov process of total spins
The Markov property for generalized gaussian random fields
We obtain necessary and sufficient conditions in order that a Gaussian process of many parameters (more generally, a generalized Gaussian random field in ) possess the Markov property relative to a class of open sets. The method adopted is the Hilbert space approach initiated by Cartier and Pitt. Applications are discussed.
The Martin Boundary for Harmonic Functions on Groups of Automorphisms of a Homogeneous Tree.
The Martin entrance boundary of the Galton–Watson process
The martingale problem for a class of pseudo differential operators.
The martingale problem with sticky reflection conditions, and a system of particles interacting at the boundary
The mass of sites visited by a random walk on an infinite graph.
The Max-Plus Martin boundary.
The McKean stochastic game driven by a spectrally negative Lev́y process.
The M/M/1 queue is Bernoulli
The classical output theorem for the M/M/1 queue, due to Burke (1956), states that the departure process from a stationary M/M/1 queue, in equilibrium, has the same law as the arrivals process, that is, it is a Poisson process. We show that the associated measure-preserving transformation is metrically isomorphic to a two-sided Bernoulli shift. We also discuss some extensions of Burke's theorem where it remains an open problem to determine if, or under what conditions, the analogue of this result...
The modification of the Galton-Watson process.
The moments of the area under reflected Brownian bridge conditional on its local time at zero.
The multifractal structure of super-brownian motion
The Nagaev-Guivarc’h method via the Keller-Liverani theorem
The Nagaev-Guivarc’h method, via the perturbation operator theorem of Keller and Liverani, has been exploited in recent papers to establish limit theorems for unbounded functionals of strongly ergodic Markov chains. The main difficulty of this approach is to prove Taylor expansions for the dominating eigenvalue of the Fourier kernels. The paper outlines this method and extends it by stating a multidimensional local limit theorem, a one-dimensional Berry-Esseen theorem, a first-order Edgeworth expansion,...
The noise made by a Poisson snake.
The norm estimate of the difference between the Kac operator and Schrödinger semigroup. II: The general case including the relativistic case.