A large deviation principle is proved for Toeplitz quadratic forms of centred stationary Gaussian processes. The rate function is obtained by a sharp study of the behaviour of eigenvalues of a product of two Toeplitz matrices. Some statistical applications such as the likelihood ratio test and...

We consider the path-valued process called the Brownian snake, conditioned so that its lifetime process is a normalised Brownian excursion. This process denoted by ((Ws, [xi]s); s [set membership, variant] [0, 1]) is closely related to the integrated super-Brownian excursion studied recently by...

We study the tail behaviour of the supremum of sample paths of Lévy process with exponential tail of the Lévy measure. Our approach is based on the theory of sojourn times developed by S. Berman. It allows us to compute the value of the limit of the ratio P(sup0<t<1 X(t) > x)/[varrho](x, [infinity]) as x...</t<1>

We derive functional limit theorems for the integrated periodogram of linear processes whose innovations may have finite or infinite variance, and which may exhibit long memory. The results are applied to obtain corresponding Kolmogorov-Smirnov and Cramér-von Mises goodness-of-fit tests.

A new least-squares approach to information dimension estimation of the invariant distribution of a dynamical system is suggested. It is computationally similar to the Grassberger-Procaccia algorithm for estimating the correlation dimension over a fixed range of radii. Under mixing assumptions...

The paper develops in different directions the method of the second author for estimation of the rate of exponential convergence of nonhomogeneous birth-death processes. Applying the method to mean-field models, we discover some phenomena related to their spectral gaps.

We develop a technique for derivation of the asymptotic joint distribution of the sample partial autocorrelations of a process, given the corresponding distribution of sample autocorrelations. No assumption of asymptotic normality is needed. The underlying process need not be stationary. The...

We study the long-term translation and dispersion of a mass distribution carried by an isotropic Brownian flow on . We use the variance of the center of mass as a measure of translation and the mean of the centered spatial second moments as a measure of dispersion. We find the exact growth rates...

For stochastic differential equations (SDEs) of the form dX(t) = b(X)(t)) dt + [sigma] (X(t))dW(t) where b and [sigma] are Lipschitz continuous, it is shown that if we consider a fixed [sigma] [epsilon] C5, bounded and with bounded derivatives, the random field of solutions is pathwise locally...

We consider the sequence of fluctuation processes associated with the empirical measures of the interacting particle system approximating the d-dimensional McKean-Vlasov equation and prove that they are tight as continuous processes with values in a precise weighted Sobolev space. More...