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Stochastic differential equations driven by $$G$$-Brownian motion with reflecting boundary conditions. (English) Zbl 1304.60068
The author considers a $$G$$-Brownian motion, stochastic integrals with respect to a $$G$$-Brownian motion and with respect to an increasing process, and a reflected $$G$$-Brownian motion. He proves the $$G$$-Itō formula.
These results are used to show the existence and uniqueness of the solution $$(X,K)$$ to the stochastic differential equation driven by the $$G$$-Brownian motion: $X_t= x+\int^t_0 f_s(X_s)\,ds+ \int^t_0 h_s(X_s)\,d\langle B\rangle_s+ \int^t_0 g_s(X_s)\,dB_s+ K_t,\tag{1}$ $$0\leq t\leq T$$, where $$x$$ is the initial condition, $$\langle B\rangle$$ is the quadratic variation process of the $$G$$-Brownian motion $$B$$, and $$K$$ is an increasing process. The coefficients $$f, h, g$$ satisfy a Lipschitz condition.
The author also establishes a comparison principle for solutions of (1).

##### MSC:
 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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