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Chen, Hong

doi:10.1023/a:1018937103955

Annals of Operations Research

1999

DOI: 10.1023/a:1018937103955

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Hong Chen¹

Abstract: The basic adjoint relation (BAR) was first introduced by Harrison and Williams [21,22] to characterize the stationary distribution of a diffusion process. Through simple examples, we show that this procedure can be used to characterize both the stationary and the transient distributions of a diffusion process, as well as other non-diffusion Markov processes.

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2020

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Green’s Functions with Oblique Neumann Boundary Conditions in the Quadrant

Franceschi

2020

J Theor Probab

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We study semi-martingale obliquely reflected Brownian motion (SRBM) with drift in the first quadrant of the plane in the transient case. Our main result determines a general explicit integral expression for the moment generating function of Green's functions of this process. To that purpose we establish a new kernel functional equation connecting moment generating functions of Green's functions inside the quadrant and on its edges. This is reminiscent of the recurrent case where a functional equation derives from the basic adjoint relationship which characterizes the stationary distribution. This equation leads us to a non-homogeneous Carleman boundary value problem. Its resolution provides a formula for the moment generating function in terms of contour integrals and a conformal mapping.

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Green’s Functions with Oblique Neumann Boundary Conditions in the Quadrant

Franceschi

2020

J Theor Probab

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Cited by 1 publication

References 32 publications

Green’s Functions with Oblique Neumann Boundary Conditions in the Quadrant

Green’s Functions with Oblique Neumann Boundary Conditions in the Quadrant

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