Stochastic Sub-Additivity Approach to the Conditional Large Deviation Principle

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...

Large deviation principle for stochastic integrals and stochastic differential equations driven by infinite dimensional semimartingales

Let H be a separable Banach space. We considered the sequence of stochastic integrals {Xn− · Yn} where {Yn} is a sequence of infinite dimesnional H semimartingales and Xn are H valued cadlag processes. Assuming that {(Xn, Yn)} satisfies large deviation principle, a uniform exponential tightness condition is described under which large deviation principle holds for {(Xn, Yn, Xn− · Yn)}. When H i...

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...

Large deviation principle for enhanced Gaussian processes

We study large deviation principles for Gaussian processes lifted to the free nilpotent group of step N . We apply this to a large class of Gaussian processes lifted to geometric rough paths. A large deviation principle for enhanced (fractional) Brownian motion, in Hölderor modulus topology, appears as special case. © 2007 Elsevier Masson SAS. All rights reserved. Résumé Nous etudions les princ...

Large deviation principle in logarithmic potential theory