Large deviations principles of Non-Freidlin-Wentzell type

TL;DR

This paper extends classical large deviation principles to Colombeau-Ito SDEs with random coefficients, incorporating jump phenomena in financial markets from first principles, without relying on Poisson processes.

Contribution

It significantly broadens the classical theory of large deviations for randomly perturbed systems, introducing a generalized approach for jumps in financial models from first principles.

Findings

Developed generalized large deviation principles for Colombeau-Ito SDEs.

Explained jumps in financial markets from first principles, avoiding Poisson processes.

Expanded the classical Freidlin-Wentzell theory to include jump phenomena.

Abstract

Generalized Large deviation principles was developed for Colombeau-Ito SDE with a random coefficients. We is significantly expand the classical theory of large deviations for randomly perturbed dynamical systems developed by Freidlin and Wentzell.Using SLDP approach, jumps phenomena, in financial markets, also is considered. Jumps phenomena, in financial markets is explained from the first principles, without any reference to Poisson jump process. In contrast with a phenomenological approach we explain such jumps phenomena from the first principles, without any reference to Poisson jump process.