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Summary: The Annals of Probability
2003, Vol. 31, No. 4, 20822108
© Institute of Mathematical Statistics, 2003
LINEAR STOCHASTIC DIFFERENTIAL EQUATIONS WITH
FUNCTIONAL BOUNDARY CONDITIONS
BY AURELI ALABERT1 AND MARCO FERRANTE2
Universitat Auṭnoma de Barcelona and Università degli Studi di Padova
We consider linear nth order stochastic differential equations on [0,1],
with linear boundary conditions supported by a finite subset of [0,1]. We
study some features of the solution to these problems, and especially its
conditional independence properties of Markovian type.
1. Introduction. It is well known that, under suitable Lipschitz and growth
conditions on the coefficients, a classical Itô stochastic differential equation
X(t) = +
t
0
b s,X(s) ds +
t
0
s,X(s) dW(s),(1.1)
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