Large deviations for Markov processes with discontinuous statistics, II: random walks

TLDR: In this paper, the authors proved the large deviation principle for a random walk whose transition mechanism is governed by a Borel probability measure on ℝ>>\s with finite moment generating functions.

Abstract: Letμ 1 andμ 2 be Borel probability measures on ℝ d with finite moment generating functions. The main theorem in this paper proves the large deviation principle for a random walk whose transition mechanism is governed byμ 1 when the walk is in the left halfspace Λ1 = {x∈ℝ d :x 1≦0} and whose transition mechanism is governed byμ 2 when the walk is in the right halfspace Λ2 = {x∈ℝ d :x 1>0}. When the measuresμ 1 andμ 2 are equal, the main theorem reduces to Cramer's Theorem.