Existence of Solutions for G-SFDEs with Cauchy-Maruyama Approximation Scheme release_d72xxdwwgbgupatek3apuwfmw4

by Faiz Faizullah

Published in Abstract and Applied Analysis by Hindawi Limited.

2014   Volume 2014, p1-8

Abstract

We present the Cauchy-Maruyama (CM) approximation scheme and establish the existence theory of stochastic functional differential equations driven by G-Brownian motion (G-SFDEs). Several useful properties of Cauchy-Maruyama (CM) approximate solutions<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msup><mml:mrow><mml:mi>X</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>of G-SFDEs are given. We show that the unique solution of G-SFDEs gets convergence from Cauchy-Maruyama (CM) approximate solutions. The existence theorem for G-SFDEs is developed with the above mentioned scheme.
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