Related papers: Moderate, large and super large deviations princip…
We investigate the Large Deviation behavior in small time of continuous Gaussian processes. We introduce a general procedure allowing to derive Large Deviation Principles in small time starting from the well understood context of Large…
Scaling laws arise and are eulogized across disciplines from natural to social sciences for providing pithy, quantitative, `scale-free', and `universal' power law relationships between two variables. On a log-log plot, the power laws…
We consider a class of slow-fast processes on a connected complete Riemannian manifold $M$.The limiting dynamics as the scale separation goes to $\infty$ is governed by the averaging principle. Around this limit, we prove large deviation…
This paper deals with Poisson processes on an arbitrary measurable space. Using a direct approach, we derive formulae for moments and cumulants of a vector of multiple Wiener-It\^o integrals with respect to the compensated Poisson process.…
The paper concerns itself with establishing large deviation principles for a sequence of stochastic integrals and stochastic differential equations driven by general semimartingales in infinite-dimensional settings. The class of…
We apply scaling and the theory of the fundamental limits of the second-order molecular susceptibility to identify material classes with ultralarge nonlinear-optical response. Size effects are removed by normalizing all nonlinearities to…
This work concerns generalized backward stochastic differential equations, which are coupled with a family of reflecting diffusion processes. First of all, we establish the large deviation principle for forward stochastic differential…
Particle approximations for certain nonlinear and nonlocal reaction-diffusion equations are studied using a system of Brownian motions with killing. The system is described by a collection of i.i.d. Brownian particles where each particle is…
We establish, under the Cramer exponential moment condition in a neighbourhood of zero, the Extended Large Deviation Principle for the Random Walk and the Compound Poisson processes in the metric space $\V$ of functions of finite variation…
We establish large deviation principles for the couple of the maximum likelihood estimators of dimensional and drift coefficients in the generalised squared radial Ornstein-Uhlenbeck process. We focus our attention to the most tractable…
We study the large deviations principle for locally periodic stochastic differential equations with small noise and fast oscillating coefficients. There are three possible regimes depending on how fast the intensity of the noise goes to…
The Moderate Deviations Principle (MDP) is well-understood for sums of independent random variables, worse understood for stationary random sequences, and scantily understood for random fields. Here it is established for splittable random…
In this paper, we proved moderate deviation principles for a fully coupled two-time-scale stochastic systems, where the slow process is given by stochastic differential equations with small noise, while the fast process is a rapidly…
Large deviations principle is obtained for terminating multidimensional compound renewal processes. We also obtained the asymptotic of large deviations for the case when a Gibbs change of the original probability measure takes place. The…
How do large deviation events in a stationary process cluster? The answer depends not only on the type of large deviations, but also on the length of memory in the process. Somewhat unexpectedly, it may also depend on the tails of the…
The large deviation principle is established for the distributions of a class of generalized stochastic porous media equations for both small noise and short time.
Polarization phenomena are essential for the understanding of elementary processes, and are typically large in the threshold region. The selection rules with respect to P-parity, angular momentum, isotopic spin and the Pauli principle allow…
A large deviation principle is derived for stochastic partial differential equations with slow-fast components. The result shows that the rate function is exactly that of the averaged equation plus the fluctuating deviation which is a…
We study the large deviations statistics of the intensive work done by changing globally a control parameter in a thermally isolated quantum many-body system. We show that, upon approaching a critical point, large deviations well below the…
An analogue of Talagrand's convex distance for binomial and Poisson point processes is defined. A corresponding large deviation inequality is proved.