Large deviations principle for a large class of one-dimensional Markov processes (Q1930529)

The paper studies the large deviation principle for Markov processes whose infinitesimal generator is \(\varepsilon {D_u}{D_v}\), where \(v\) and \(u\) are two strictly increasing functions, \(v\) right-continuous, \(u\) continuous, and \(0 < \varepsilon \ll 1\). These results generalize the classical large deviation results for a large class of one-dimensional strong Markov processes that can not be expressed as solutions to stochastic differential equations. Furthermore, the paper considers the problem of wavefront propagation for reaction-diffusion equations governed by a generalized operator \({D_u}{D_v}\).