Fixed point technique for a class of backward stochastic differential equations

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Authors
Romeo Negrea
 Department of Mathematics, Politehnica University of Timisoara, Pta Victoriei 2, Timisoara, 300006, Romania.
Ciprian Preda
 Faculty of Economics and Business Administration, West University of Timisoara, Bd. V. Parvan 4, Timisoara, 300223, Romania.
Abstract
We establish a new theorem on the existence and uniqueness of the adapted solution to backward stochastic
differential equations under some weaker conditions than the Lipschitz one. The extension is based on
Athanassov's condition for ordinary differential equations. In order to prove the existence of the solutions
we use a fixed point technique based on Schauder's fixed point theorem. Also, we study some regularity
properties of the solution for this class of stochastic differential equations.
Share and Cite
ISRP Style
Romeo Negrea, Ciprian Preda, Fixed point technique for a class of backward stochastic differential equations, Journal of Nonlinear Sciences and Applications, 6 (2013), no. 1, 4150
AMA Style
Negrea Romeo, Preda Ciprian, Fixed point technique for a class of backward stochastic differential equations. J. Nonlinear Sci. Appl. (2013); 6(1):4150
Chicago/Turabian Style
Negrea, Romeo, Preda, Ciprian. "Fixed point technique for a class of backward stochastic differential equations." Journal of Nonlinear Sciences and Applications, 6, no. 1 (2013): 4150
Keywords
 Backward stochastic differential equations
 nonLipschitz conditions
 adapted solutions
 pathwise uniqueness
 global solutions
 fixed point technique
 Schauder's fixed point theorem.
MSC
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