Existence and uniqueness of solutions of stochastic functional differential equations
نویسندگان
چکیده
منابع مشابه
Existence and uniqueness of solutions of stochastic functional differential equations
We provide sufficient conditions on the coefficients of a stochastic functional differential equation with bounded memory driven by Brownian motion which guarantee existence and uniqueness of a maximal local and global strong solution for each initial condition. Our results extend those of previous works. For local existence and uniqueness, we only require the coefficients to be continuous and ...
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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 pa...
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ژورنال
عنوان ژورنال: Random Operators and Stochastic Equations
سال: 2010
ISSN: 0926-6364,1569-397X
DOI: 10.1515/rose.2010.015