Pluripotential energy and large deviation

Sharp Large Deviation for the Energy of α-Brownian Bridge

where W is a standard Brownian motion, t ∈ [0, T), T ∈ (0,∞), and the constant α > 1/2. Let P α denote the probability distribution of the solution {X t , t ∈ [0, T)} of (1). The α-Brownian bridge is first used to study the arbitrage profit associatedwith a given future contract in the absence of transaction costs by Brennan and Schwartz [1]. α-Brownian bridge is a time inhomogeneous diffusion ...

Large deviation theory and applications

Large deviation theory deals with the decay of the probability of increasingly unlikely events. It is one of the key techniques of modern probability, a role which is emphasised by the recent award of the Abel prize to S.R.S. Varadhan, one of the pioneers of the subject. The subject is intimately related to combinatorial theory and the calculus of variations. Applications of large deviation the...

Functional Large Deviation

We establish functional large deviation principles (FLDPs) for waiting and departure processes in single-server queues with unlimited waiting space and the rst-in rst-out service discipline. We apply the extended contraction principle to show that these processes obey FLDPs in the function space D with one of the non-uniform Skorohod topologies whenever the arrival and service processes obey FL...

Large Deviation Theory

If we draw a random variable n times from Q, the probability distribution of the sum of the random variables is given by Q. This is the convolution of Q with itself n times. As n → ∞, Q tends to a normal distribution by the central limit theorem. This is shown in Figure 1. The top line is a computed normal distribution with the same mean as Q. However, as shown in Figure 3, when plotted on a lo...

Thermodynamic Formalism, Large Deviation, and Multifractals