Nonlinear large deviations

Large Deviations for Markovian Nonlinear Hawkes Processes

In the 2007 paper, Bordenave and Torrisi [1] proves the large deviation principles for Poisson cluster processes and in particular, the linear Hawkes processes. In this paper, we prove first a large deviation principle for a special class of nonlinear Hawkes process, i.e. a Markovian Hawkes process with nonlinear rate and exponential exciting function, and then generalize it to get the result f...

Large Deviations for Stochastic Nonlinear Beam Equations

We establish a large deviation principle for the solutions of stochastic partial differential equations for nonlinear vibration of elastic panels (also called stochastic nonlinear beam equations).

Quenched Large Deviations for One Dimensional Nonlinear Filtering

Consider the standard, one dimensional, nonlinear filtering problem for diffusion processes observed in small additive white noise: dXt = b(Xt)dt + dBt , dY ε t = γ(Xt)dt + εdVt , where B·, V· are standard independent Brownian motions. Denote by qε 1(·) the density of the law of Ξ1 conditioned on σ(Y ε t : 0 ≤ t ≤ 1). We provide “quenched” large deviation estimates for the random family of meas...

Process-level Large Deviations for Nonlinear Hawkes Point Processes

In this paper, we prove a process-level, also known as level-3 large deviation principle for a very general class of simple point processes, i.e. nonlinear Hawkes process, with a rate function given by the process-level entropy, which has an explicit formula.

Large Deviations