Moment inequalities for locally square integrable martingales are considered. The growth rates of the constants in Rosenthal's inequality for locally square integrable martingales and Burkholder-Gundy inequality for martingales with symmetric jumps are given.

Let (Xn)n[greater-or-equal, slanted]1 be a sequence of real random variables. The local score is Hn=max1[less-than-or-equals, slant]i<j[less-than-or-equals, slant]n (Xi+...+Xj). If (Xn)n[greater-or-equal, slanted]1 is a "good" Markov chain under its invariant measure, the Xi are centered, we prove that converges in distribution to B1* when n-->+[infinity], where B1*=max0[less-than-or-equals, slant]u[less-than-or-equals, slant]1 Bu and (Bu,u[greater-or-equal, slanted]0) is a standard Brownian motion,...</j[less-than-or-equals,>

We consider a linear rate equation, depending on three parameters, that model fragmentation. For each of these fragmentation equations, there is a corresponding stochastic model, from which we construct an explicit solution to the equation. This solution is proved unique. We then use this...

We give a proof of Fatou's Theorem for censored [alpha]-stable processes in a bounded C1,1 open set D where [alpha][set membership, variant](1,2). As an application of Fatou's Theorem, we show that the harmonic measure for such censored [alpha]-stable process is mutually absolutely continuous...

In this paper we study the relationships between two Markov Chain Monte Carlo algorithms--the Swapping Algorithm (also known as the Metropolis-coupled algorithm) and the simulated tempering algorithm. We give a proof that the spectral gap of the simulated tempering chain is bounded below by a...

A comprehensive description is given of the limiting behaviour of normalised pseudo-MLEs of the coefficients in a discrete-time autoregressive process, with nonstochastic regressors, for all cases: stationary, unit root and explosive situations. The residuals are assumed to be independent and...

We consider a discrete time Markov chain whose state space is the set of all NxN stochastic matrices with zero diagonal entries. This chain models the evolution of relationships among N individuals who exchange gifts according to probabilities determined by previous exchanges. We determine the...

We prove a uniform Poincaré inequality for non-interacting unbounded spin systems with a conservation law, when the single-site potential is a bounded perturbation of a convex function with polynomial growth at infinity. The result is then applied to Ginzburg-Landau processes to show diffusive...

In the present article, we will consider a conditional limit theorem and conditional asymptotic expansions. Our discussion will be based on the Malliavin calculus. First, we treat a problem of lifting limit theorems to their conditional counterparts. Next, we provide asymptotic expansions in a...

We consider fractional Brownian motions BtH with arbitrary Hurst coefficients 0H1 and prove the following results: (i) An integral representation of the fractional white noise as generalized Wiener integral; (ii) an Itô formula for generalized functionals of BtH; (iii) an analogue of Tanaka's...