Large Deviation Principle for a Stochastic Heat Equation With Spatially Correlated Noise

Stochastic heat equation with white-noise drift

A large deviation principle with queueing applications

In this paper, we present a large deviation principle for partial sums processes indexed by the half line, which is particularly suited to queueing applications. The large deviation principle is established in a topology that is finer than the topology of uniform convergence on compacts and in which the queueing map is continuous. Consequently, a large deviation principle for steady-state queue...

A large deviation principle for Dirichlet posteriors

Let Xk be a sequence of independent and identically distributed random variables taking values in a compact metric space Ω, and consider the problem of estimating the law of X1 in a Bayesian framework. A conjugate family of priors for non-parametric Bayesian inference is the Dirichlet process priors popularized by Ferguson. We prove that if the prior distribution is Dirichlet, then the sequence...

A large deviation principle for Dirichlet posteriorsA

Let X k be a sequence of independent and identically distributed random variables taking values in a compact metric space , and consider the problem of estimating the law of X 1 in a Bayesian framework. A conjugate family of priors for non-parametric Bayesian inference is the Dirichlet process priors popularized by Ferguson. We prove that if the prior distribution is Dirichlet, then the sequenc...

Stochastic Sub - Additivity Approach to the Conditional Large Deviation Principle

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...