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An integro-differential equation for the probability density of thegeneralized stochastic Ornstein-Uhlenbeck process with jump diffusion isconsidered. It is shown that for a certain ratio between the intensity of jumpsand the speed of reversion, the fundamental solution can be found explicitly.The properties of this solution are investigated. The fundamental solutionallows one to obtain explicit formulas for the densities at each moment oftime.

An explicit form of the fundamental solution of the master equation for a jump-diffusion Ornstein-Uhlenbeck process