In the article Quenched large deviation principle for words in a letter sequence, Probab. Theory Relat. Fields 148, no. 3/4 (2010), 403–456 we derived quenched empirical process of obtained by cutting an i.i.d. sequence letters according to independent renewal process. We representation associated rate function stationary word processes terms certain specific relative entropies. Our proof this ...

We consider level-2 large deviations for the one-sided countable full shift without assuming existence of Bowen's Gibbs state. To deal with non-compact closed sets, we provide a sufficient condition in terms inducing which ensures exponential tightness sequence Borel probability measures constructed from periodic configurations. Under this establish Large Deviation Principle. apply our results ...

In this paper, we first prove that the large deviation principle is preserved under a homeomorphism. As an application, establish for distribution dependent stochastic differential equations with Dini continuous drift, semilinear partial respectively.

The present work deals with the global solvability as well asymptotic analysis of stochastic generalized Burgers–Huxley (SGBH) equation perturbed by a white-in-time and correlated-in-space noise defined in bounded interval $${\mathbb {R}}$$ . We first prove existence unique mild strong solution to SGBH then obtain an invariant measure. Later, we establish two major properties Markovian semigrou...

We prove a large deviation principle (LDP) for greedy exploration process on an Erdos-Renyi (ER) graph when the number of nodes goes to this http URL our main result we use general strategy study deviations processes proposed by Feng and Kurtz (2006), which is based convergence non-linear semigroups. The rate function can be expressed in closed form formula associated optimization problems solv...

In the 2007 paper, Bordenave and Torrisi [1] proves the large deviation principles for Poisson cluster processes and in particular, the linear Hawkes processes. In this paper, we prove first a large deviation principle for a special class of nonlinear Hawkes process, i.e. a Markovian Hawkes process with nonlinear rate and exponential exciting function, and then generalize it to get the result f...

We investigate the large deviation properties of the maximum likelihood estimators for the Ornstein-Uhlenbeck process with shift. We propose a new approach to establish large deviation principles which allows us, via a suitable transformation, to circumvent the classical non-steepness problem. We estimate simultaneously the drift and shift parameters. On the one hand, we prove a large deviation...