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.

Some remarks on First-Passage-Time for Jump-Diffusion Processes

GIRAUDO, Maria Teresa;SACERDOTE, Laura Lea
1996

Abstract

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.
European Meeting on Cybernetics and Systems Research
Università di Vienna
9-12 Aprile 1996
Cybernetics and Systems 96
Austrian Society for Cybernetic Studies
1
518
523
9783852061337
Moments; Ornstein-Uhlenbeck process; Feller process; Laplace transform
M. GIRAUDO; SACERDOTE L.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2318/18306
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