We consider semiparametric fractional exponential (FEXP) estimators of the memory parameter d for a potentially non-stationary linear long-memory time series with additive polynomial trend. We use differencing to annihilate the polynomial trend, followed by tapering to handle the potential...

The ergodic properties of SDEs, and various time discretizations for SDEs, are studied. The ergodicity of SDEs is established by using techniques from the theory of Markov chains on general state spaces, such as that expounded by Meyn-Tweedie. Application of these Markov chain results leads to...

We consider a conservative stochastic lattice gas dynamics reversible with respect to the canonical Gibbs measure of the bond dilute Ising model on at inverse temperature [beta]. When the bond dilution density p is below the percolation threshold, we prove that, for any [var epsilon]0, any...

Let Xt=[summation operator]k=-[infinity]+[infinity]ak([var epsilon]t-k) be a linear process with values in a Hilbert space H. The H valued r.v. [var epsilon]k are i.i.d. centered, the ak's are linear operators. We prove a central limit theorem for the vector of empirical covariance operators of...

Using the Malliavin Calculus, this paper proves the existence of a weak function-solution of class with bounded derivatives of the Landau equation for a generalization of Maxwellian molecules when the initial data is a probability measure.

Fleischmann and Mueller (Probab. Theory Related Fields 107 (1997) 325) constructed a super-Brownian motion in R1 with a locally infinite branching rate function, and they showed that this super-Brownian motion has a strong killing property in the critical case. In this paper, we first construct,...

The theory of general state-space Markov chains can be strongly related to the case of discrete state-space by use of the notion of small sets and associated minorization conditions. The general theory shows that small sets exist for all Markov chains on state-spaces with countably generated...

In this paper, we study the robustness of backward stochastic differential equations (BSDEs for short) w.r.t. the Brownian motion; more precisely, we will show that if Wn is a martingale approximation of a Brownian motion W then the solution to the BSDE driven by the martingale Wn converges to...

Fractals and measures are often defined in a constructive way. In this paper, we give the construction of random measures concentrated on random Markov-self-similar fractals and prove that under quite weak conditions random Markov-self-similar measures exist and satisfy certain self-similarity...

The diffusive coagulation equation models the evolution of the local concentration n(t,x,z) of particles having position and size z at time t, for a system in which a coagulation phenomenon occurs. The aim of this paper is to introduce a probabilistic approach and a numerical scheme for this...