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Z. Naturforsch. 67a, 699 – 704 (2012)
doi:10.5560/ZNA.2012-0079
A Note on the Carathéodory Approximation Scheme for Stochastic Differential Equations under G-Brownian Motion
Faiz Faizullah
Department of Basic Sciences and Humanities, College of Electrical and Mechanical Engineering, National University of Sciences and Technology, Pakistan
Received June 5, 2012 / revised August 6, 2012 / published online November 14, 2012
Reprint requests to: F. F.; E-mail: faiz_math@yahoo.com
In this note, the Carathéodory approximation scheme for vector valued stochastic differential equations under G-Brownian motion (G-SDEs) is introduced. It is shown that the Carathéodory approximate solutions converge to the unique solution of the G-SDEs. The existence and uniqueness theorem for G-SDEs is established by using the stated method.
Key words: Stochastic Differential Equations; G-Brownian Motion; Carathéodory's Approximation Scheme; Existence; Uniqueness.
Mathematics Subject Classification 2000: 60H10; 60H20; 60H35; 62L20
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