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Stochastic Processes and their Applications 91 (2001) 255276 www.elsevier.com/locate/spa
 

Summary: Stochastic Processes and their Applications 91 (2001) 255­276
www.elsevier.com/locate/spa
Di erential equations with boundary conditions perturbed
by a Poisson noise
Aureli Alabert ;1
, Miguel A. Marmolejo 2
Departament de MatemÂatiques, Universitat AutÂonoma de Barcelona, E-08193-Bellaterra,
Catalonia, Spain
Received 6 March 2000; received in revised form 27 June 2000; accepted 5 July 2000
Abstract
We consider one-dimensional di erential equations with a boundary condition on the interval
[0; 1], perturbed by a Poisson noise. We study existence and uniqueness, the law of the solution
and in which cases the solution is a reciprocal process. c 2001 Elsevier Science B.V. All rights
reserved.
MSC: 60H10; 60J25; 34F05
Keywords: Stochastic di erential equations; Boundary conditions; Reciprocal processes; Poisson
noise
1. Introduction
In the last years some papers have been written on stochastic di erential equations
with boundary conditions driven by a white noise, namely, problems of the form

  

Source: Alabert, Aureli - Departament de Matemàtiques, Universitat Auṭnoma de Barcelona

 

Collections: Mathematics