Fixed point technique for a class of backward stochastic differential equations
- Department of Mathematics, Politehnica University of Timisoara, P-ta Victoriei 2, Timisoara, 300006, Romania.
- Faculty of Economics and Business Administration, West University of Timisoara, Bd. V. Parvan 4, Timisoara, 300223, Romania.
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.
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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, 41--50
Negrea Romeo, Preda Ciprian, Fixed point technique for a class of backward stochastic differential equations. J. Nonlinear Sci. Appl. (2013); 6(1):41--50
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): 41--50
- Backward stochastic differential equations
- non-Lipschitz conditions
- adapted solutions
- pathwise uniqueness
- global solutions
- fixed point technique
- Schauder's fixed point theorem.
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