While simple diffusion processes heve been the object of a careful study over the last years, a wide range of interesting problems in applications exists for which it seems appropriate to consider a more complex model. In particular, jumps occurring at random distributed instants of time can be superimposed on a simple diffusion generating what is called a jump-diffusion process. Here we present an attempt to study such models in an analytical form. We formulate new integral equations for the moments of first-passage-time in the case of constant amplitude Poisson time distributed jumps and express the moments in term of the Laplace transform of simple diffusion first-passage-time density in some other modelling interesting instances.
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