Existence of Solutions for Stochastic Differential Equations under G-Brownian Motion with Discontinuous Coefficients
2012 ◽
Vol 67
(12)
◽
pp. 692-698
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Keyword(s):
The existence theory for the vector valued stochastic differential equations under G-Brownian motion (G-SDEs) of the type Xt = X0+ ∫to(v;Xv)dv+ ∫t0 g(v;Xv)d(B)v+ ∫t0 h(v;Xv)dBv; t ∊ [0;T]; with first two discontinuous coefficients is established. It is shown that the G-SDEs have more than one solution if the coefficient g or the coefficients f and g simultaneously, are discontinuous functions. The upper and lower solutions method is used and examples are given to explain the theory and its importance.
2014 ◽
Vol 50
(8)
◽
pp. 1053-1069
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2012 ◽
Vol 67
(12)
◽
pp. 699-704
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2006 ◽
Vol 2006
◽
pp. 1-6
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2021 ◽
Vol 37
(7)
◽
pp. 1156-1170
2019 ◽
Vol 20
(03)
◽
pp. 2050015
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