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

Francesco RUSSO     Stochastic Differential Equations (SDEs)   (format .ps compressé)

Résumé: This paper will appear in "Encyclopedia of Mathematical Physics", see 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

  • Martingales with continuous parameter ;  60H10
  • Stochastic ordinary differential equations, See Also { ;  60H15
  • Stochastic partial differential equations, See also {35R60} ;  60J60
  • Diffusion processes, See also {58G32} ; 

    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