Large deviation principles are proved for rescaled Poisson random measures. As a consequence, Freidlin-Wentzell type large deviations results for processes with independent increments are obtained in situations where exponential moments are infinite.

We develop a new method to obtain stochastic characterizations of Yang-Mills fields. Our main tool is the Itô-equation for the stochastic parallel transport. We estimate the drift terms in a small ball of radius [var epsilon] and find that for a general connection the average rotation is of...

We study a parabolic SPDE driven by a white noise and a compensated Poisson measure. We first define the solutions in a weak sense, and we prove the existence and the uniqueness of a weak solution. Then we use the Malliavin calculus in order to show that under some non-degeneracy assumptions,...

We develop a new approach for proving large deviation results for martingales based on a change of probability measure. It extends to the case of martingales the conjugate distribution technique due to Cramér. To demonstrate our approach, we derive formulae for probabilities of large deviations...

Sufficient conditions for a rank-dependent moderate deviations principle (MDP) for degenerate U-processes are presented. The MDP for VC classes of functions is obtained under exponential moments of the envelope. Among other techniques, randomization, decoupling inequalities and integrability of...

We consider the problem of maximizing the expected logarithmic utility from consumption or terminal wealth in a general semimartingale market model. The solution is given explicitly in terms of the semimartingale characteristics of the securities price process.

The conditional Feynman-Kac functional is used to derive the Laplace transforms of conditional maximum distributions of processes related to third- and fourth-order equations. These distributions are then obtained explicitly and are expressed in terms of stable laws and the fundamental solutions...

Classical super-Brownian motion (SBM) is known to take values in the space of absolutely continuous measures only if d=1. For d[greater-or-equal, slanted]2 its values are almost surely singular with respect to Lebesgue measure. This result has been generalized to more general motion laws and...

We consider a generalized Mandelbrot's martingale {Yn} and the associated Mandelbrot's measure [mu][omega] on marked trees. If the limit variable Z=lim Yn is not degenerate, we study the asymptotic behavior at infinity of its distribution; in the contrary case, we prove that there is an...

We consider the anharmonic crystal, or lattice massless field, with 0-boundary conditions outside and N a large natural number, that is the finite volume Gibbs measure on for every x[negated set membership]DN} with Hamiltonian [summation operator]x~yV([phi]x-[phi]y), V a strictly convex even...