Squared radial Ornstein-Uhlenbeck processes and inverse Laplace transforms of products of confluent hypergeometric functions

Abstract

In this paper, we consider the squared radial Ornstein-Uhlenbeck process and associated Kolmogorov backward equation (the Laguerre heat
equation). For this process, we obtain the Green function of the Laplace transform of the transition density function in terms of the confluent hypergeometric functions and present new representations for the inverse Laplace transform of the products of confluent hypergeometric functions.

Keywords

• Laplace transform,Fourier transform,Squared radial Ornestein- Uhlenbeck process,Laguerre equation,Conuent hypergeometric function

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