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Contents of PMS, Vol. 11, Fasc. 1,
pages 47 - 78
 

MOUVEMENTS BROWNIENS ASYM…TRTQUES MODIFI…S EN DIMENSION FINIE ET OP…RATEURS DIFF…RENTIELS ņ COEFFICIENTS DISCONTINUS

MichŤle Mastrangelo
Mouloud Talbi

Abstract: We consider a partial differential equation of parabolic type on E = Rd  (d  (-  N ),
      *

@u
---
@t(x,t) = Lu(x,t), x  (- E,t  (- R+, (1)
u(x,0) = f(x), u(.,t)/@E = 0
where L = (C1V + D1W )D + dSA \~/ , V and W being two subdomains of E such that E = V  U W  U  S, V  /~\ W /= ō and S being a  2
C  -variety. The functions C and D are  2
C  on E , dy is the surface-vector-measure on S , A is a function defined on S which will be precised later on, dSA is a generalized drift,  \~/  [resp.  /_\  ] is the classical gradient [resp. Laplacian operator] on  d
R  .

We give, via a modified skew Brownian motion, a stochastic resolution of (1) - L 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 S.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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