We obtain necessary and sufficient conditions in the Large Deviation Principle for random upper semicontinuous functions on a separable Banach space. The main tool is the recent work of Arcones on the LDP for empirical processes.

In this article we establish a large deviation principle for the family {ν ε : ε ∈ (0, 1)} of distributions of the scaled stochastic processes {P − log √ ε Z t } t≤1 , where (Z t) t∈[0,1] is a square-integrable martingale over Brownian filtration and (P t) t≥0 is the Ornstein-Uhlenbeck semigroup. The rate function is identified as well in terms of the Wiener-Itô chaos decomposition of the termi...

When we cut an i.i.d. sequence of letters into words according to an independent renewal process, we obtain an i.i.d. sequence of words. In the annealed large deviation principle (LDP) for the empirical process of words, the rate function is the specific relative entropy of the observed law of words w.r.t. the reference law of words. In the present paper we consider the quenched LDP, i.e., we c...

University of Chicago Given two Polish spaces AX and AY, let ρ AX × AY → d be a bounded measurable function. Let X = Xn n ≥ 1 and Y = Yn n ≥ 1 be two independent stationary processes on AX and A ∞ Y , respectively. The article studies the large deviation principle (LDP) for n−1 ∑n k=1 ρ Xk Yk , conditional on X. Based on a stochastic version of approximate subadditivity, it is shown that if Y s...

We consider a join-the-shortest-queue model which is as follows. There are K single FIFO servers and M arrival processes. The customers from a given arrival process can be served only by servers from a certain subset of all servers. The actual destination is the server with the smallest weighted queue length. The arrival processes are assumed to obey a large deviation principle while the servic...

Limit theorems, including the large deviation principle, are established for random point processes (fields), which describe the position distributions of the perfect boson gas in the regime of the Bose-Einstein condensation. We compare these results with those for the case of the normal phase.

We consider a join-the-shortest-queue model which is as follows. There are K single FIFO servers and M arrival processes. The customers from a given arrival process can be served only by servers from a certain subset of all servers. The actual destination is the server with the smallest weighted queue length. The arrival processes are assumed to obey a large deviation principle while the servic...