Generalized Rayleigh and Jacobi processes and exceptional orthogonal polynomials

TL;DR

This paper introduces four classes of exactly solvable Fokker-Planck equations linked to exceptional orthogonal polynomials, extending classical Rayleigh and Jacobi processes with new solvable models.

Contribution

It presents novel deformed Rayleigh and Jacobi processes connected to exceptional orthogonal polynomials, expanding the set of exactly solvable stochastic models.

Findings

Four types of solvable Fokker-Planck equations related to exceptional polynomials

Deformed Rayleigh and Jacobi processes constructed

New exactly solvable stochastic models introduced

Abstract

We present four types of infinitely many exactly solvable Fokker-Planck equations, which are related to the newly discovered exceptional orthogonal polynomials. They represent the deformed versions of the Rayleigh process and the Jacobi process.