Prépublication numéro 2005-23 du laboratoire LAGA, Université Paris 13 |

**Résumé:** This paper will appear in "Encyclopedia of Mathematical Physics", see
http://www1.elsevier.com/homepage/about/mrwd/emp/menu.htm.
and it constitutes a survey paper on the title subject.
"Stochastic differential equations" (SDEs) appear today
as a modeling tool in several sciences as
telecommunications, economics, finance, biology
and quantum field theory.

A stochastic differential equation is essentially a classical differential equation which is perturbed by a random noise. When nothing else is specified, SDE means in fact "ordinary" stochastic differential equation; in that case it corresponds to the perturbation of an ordinary differential equation. Stochastic partial differential equations (SPDEs) are obtained as random perturbation of "partial" differential equations.

**Code(s) de Classification MSC2000: **60G44

**Mots Clés:** *Stochastic ordinary (partial) differential equations; Feynmann-Kac formula; probabilistic representation of a
(linear or non-linear) PDE; Brownian motion; diffusion process; pathwise uniqueness; strong existence;
weak existence; uniqueness in law; Peano phenomena*

**Langue du texte: ** *Anglais *

**Article reçu:** 2005-10-13