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 surface-vector-measure 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: -
