UNIVERSITY
OF WROCŁAW
 
Main Page
Contents
Online First
General Information
Instructions for authors


VOLUMES
44.2 44.1 43.2 43.1 42.2 42.1 41.2
41.1 40.2 40.1 39.2 39.1 38.2 38.1
37.2 37.1 36.2 36.1 35.2 35.1 34.2
34.1 33.2 33.1 32.2 32.1 31.2 31.1
30.2 30.1 29.2 29.1 28.2 28.1 27.2
27.1 26.2 26.1 25.2 25.1 24.2 24.1
23.2 23.1 22.2 22.1 21.2 21.1 20.2
20.1 19.2 19.1 18.2 18.1 17.2 17.1
16.2 16.1 15 14.2 14.1 13.2 13.1
12.2 12.1 11.2 11.1 10.2 10.1 9.2
9.1 8 7.2 7.1 6.2 6.1 5.2
5.1 4.2 4.1 3.2 3.1 2.2 2.1
1.2 1.1
 
 
WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 10, Fasc. 1,
pages 57 - 63
 

SUR LES SOLUTIONS FAIBLES D’EQUATIONS DIFFERENTIELLES STOCHASTIQUES

Ouknine Youssef

Abstract: A characterization of the existence of the solutions of stochastics differential equations on R - for any initial data - has been given by Engelbert and Schmidt in [5]. In this paper we propose to give a necessary and sufficient condition for the equation


integral t Xt = x0 + s(Xs)dBs 0
(*)

to admit a weak solution. By using a theorem of convergence for continuous local martingals and its connection with the local time, we prove a lemma which generalizes theorem (3) of [3]. Then we deduce that if equation (*) admits a solution verifying <x> oo = + oo , then the diffusion coefficient s cannot vanish on strictly positive Lebesgue measure set and, if s(x0) /= 0, then -2 s is locally integrable in a neighbourhood of x0. We finish with an extending the preceding results to equations with no zero drift.

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

Key words and phrases: -

Download:    Abstract    Full text   Abstract + References