Sufficient conditions for the moderate and large deviation principle for U-processes are given. For the large deviation result the conditions are in terms of "blockwise" empirical process conditions. On the moderate scaling the case of U-processes indexed by a uniformly bounded VC subgraph class...

Stochastic partial differential equations (SPDEs) of parabolic type driven by (pure) Poisson white noise are investigated in this paper. These equations are interpreted as stochastic integral equations of the jump type involving evolution kernels. Existence and uniqueness of the solution is...

We consider Gibbs measures on the set of paths of nearest-neighbors random walks on . The basic measure is the uniform measure on the set of paths of the simple random walk on and the Hamiltonian awards each visit to site by an amount , . We give conditions on ([alpha]x) that guarantee the...

This paper is devoted to the well known transformations that preserve a large deviation principle (LDP), namely, the contraction principle with approximately continuous maps and the concepts of exponential equivalence and exponential approximations. We generalize these transformations to...

In this paper, we consider a security market in which two investors on different information levels maximize their expected logarithmic utility from terminal wealth. While the ordinary investor's portfolio decisions are based on a public information flow, the insider possesses from the beginning...

Let be i.i.d. -valued random variables. We prove partial moderate deviation principles for self-normalized partial sums subject to minimal moment assumptions. Applications to the self-normalized law of the iterated logarithm are also discussed.

The consistency and asymptotic linearity of recursive maximum likelihood estimator is proved under some regularity and ergodicity assumptions on the logarithmic derivative of a transition density for a general statistical model. © 1998 Elsevier Science B.V.

The purpose of the present paper is to prove a principle of large deviations for Brosamler's functional almost everywhere central limit theorem for i.i.d. random variables on . This principle of large deviations for the functional almost everywhere central limit theorem naturally implies a...

We now analyze the asymptotic behaviour of Xt, as t approaches infinity, X being solution of where [beta] is a given odd and increasing Lipschitz-continuous function with polynomial growth. We prove with additional assumptions on [beta] that Xt converges in distribution to the invariant...

The problem of estimating the drift of a stochastic flow given Lagrangian observations is an estimation problem for a multidimensional diffusion with a degenerate diffusion matrix. The maximum-likelihood estimator of the constant drift is considered. A long-time asymptotic of its mean-square...