Global in Time Asymptotic Solutions to Kolmogorov--Feller-Type Parabolic Pseudodifferential Equations with a Small Parameter. Forward and Backward in Time Motion

TL;DR

This paper introduces a new characteristic-based method for constructing asymptotic solutions to Kolmogorov--Feller-type parabolic pseudodifferential equations with a small parameter, applicable in both forward and backward time scenarios.

Contribution

It presents a novel approach leveraging characteristics to develop asymptotic solutions for complex parabolic PDEs with small parameters.

Findings

Successful construction of asymptotic solutions using the new method

Applicability to both forward and backward in time equations

Enhanced understanding of solution behavior in small parameter regimes

Abstract

The goal of the present paper is to present a new approach to the construction of asymptotic (approximating) solutions to parabolic PDE by using the characteristics.