Open AccessUniqueness of Solutions of Stochastic Differential Equations
Author(s) -
A. M. Davie
Publication year - 2007
Publication title -
international mathematics research notices
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.757
H-Index - 76
eISSN - 1687-0247
pISSN - 1073-7928
DOI - 10.1093/imrn/rnm124
Subject(s) - mathematics , stochastic differential equation , uniqueness , brownian motion , bounded function , mathematical analysis , differential equation , function (biology) , wiener process , mathematical physics , pure mathematics , statistics , biology , evolutionary biology
It follows from a theorem of Veretennikov [4] that (1) has a unique strong solution, i.e. there is a unique process x(t), adapted to the filtration of the Brownian motion, satisfying (1). Veretennikov in fact proved this for a more general equation. Here we consider a different question, posed by N. V. Krylov [2]: we choose a Brownian path W and ask whether (1) has a unique solution for that particular path. The main result of this paper is the following affirmative answer:
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