MOUVEMENTS BROWNIENS ASYMÉTRTQUES MODIFIÉS EN
DIMENSION FINIE ET OPÉRATEURS DIFFÉRENTIELS À COEFFICIENTS
DISCONTINUS
Michèle Mastrangelo
Mouloud Talbi
Abstract: We consider a partial differential equation of parabolic type on
(x,t)  = Lu(x,t), x E,t R_{+},  (1)

u(x,0)  = f(x), u(^{.},t)/E = 0   
where
and
being two subdomains of
such that
and
being a
variety. The functions
and
are
on
,
is the surfacevectormeasure on
,
is a function defined on
which
will be precised later on,
is a generalized drift,
[resp.
] is the classical gradient
[resp. Laplacian operator] on
.
We give, via a modified skew Brownian motion, a stochastic resolution of (1)  being
considered as a generalized infinitesimal generator  and we study the continuity properties of
the transition probability densities and of their derivatives at the neighbourhood of
2000 AMS Mathematics Subject Classification: Primary: ; Secondary: ;
Key words and phrases: 