New types of mixed large deviation and ergodic theorems are obtained for nonlinearly perturbed regenerative processes, semi-Markov processes, and continuous-time Markov chains with absorption. Applications to the analysis of pseudo-stationary phenomena for stochastic systems are discussed....

Suppose that L=[summation operator]i, j=1daij(x)[not partial differential]2/[not partial differential]xi[not partial differential]xj is uniformly elliptic. We use XL(t) to denote the diffusion associated with L. In this paper we show that, if the dimension of the set is strictly less than d, the...

The aggregation procedure when a sample of length N is divided into blocks of length m=o(N), m--[infinity] and observations in each block are replaced by their sample mean, is widely used in statistical inference. Taqqu et al. (1995, Fractals, 3, 785-798), and Teverovsky and Taqqu (1997, J. Time...

In this article sharp asymptotics for the solution of nonhomogeneous Kolmogorov, Petrovskii and Pisciunov equation depending on a small parameter are considered when the initial condition is the characteristic function of a set . We show how to extend the Ben Arous and Rouault's result that...

The stability of generally defined nonlinear time series is of interest as nonparametric and other nonlinear methods are used more and more to fit time series. We provide sufficient conditions for stability or nonstability of general nonlinear AR(1) models having delay d[greater-or-equal,...

In this paper, we study a renormalized self-collision local time for superprocesses over stable processes and classical diffusions. When the renormalization breaks down, we obtain limit theorems.

Let {Xn}n[greater-or-equal, slanted]0 be a Harris recurrent Markov chain with state space E and let [xi] be a measurable map from E to a separable Banach space B and setSome integrabilities and tail behaviors of Sn over one excursion between two visits to a subset A of E are considered. It is...

For a wide class of measures, the multifractal spectrum is shown to exist iff an appropriate large deviations principle holds, in which case the spectrum is directly obtained from the corresponding rate function. A large deviations tool, enabling the use of the Gärtner-Ellis theorem for the...

We consider two possible extensions of the standard definition of Gibbs measures for lattice spin systems. When a random field has conditional distributions which are almost surely continuous (almost Gibbsian field), then there is a potential for that field which is almost surely summable...

The random cluster model on a general infinite graph with bounded degree wired at infinity is considered and a "ghost vertex" method is introduced in order to explicitly construct random cluster measures satisfying the Dobrushin-Lanford-Ruelle condition for q[greater-or-equal, slanted]1. It is...