Large Deviation Principle for the Whittaker 2d Growth Model

Jun Gao, Jie Ding

Abstract:

Abstract: The Whittaker 2d growth model is a triangular continuous
Markov diffusion process that appears in many scientific contexts. It has
been theoretically intriguing to establish a large deviation principle for this
2d process with a scaling factor. The main challenge is the spatiotemporal interactions and dynamics that may depend on potential sample-path
intersections. We develop such a principle with a novel rate function. Our
approach is mainly based on Schider’s Theorem, contraction principle, and
special treatment for intersecting sample paths.