Stochastic Volatility: Approximation and Goodness-of-fit Test
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چکیده
Let X be the unique solution started from x0 of the stochastic differential equation dXt = θ(t, Xt)dBt + b(t, Xt)dt with B a standard Brownian motion. We consider an approximation of the volatility θ(t, Xt), the drift being considered as a nuisance parameter. The approximation is based on a discrete time observation of X and we study its rate of convergence as a process. A goodness-of-fit test is also constructed. 2000 AMS Mathematics Subject Classification: Primary: 62M05; Secondary: 62M02, 62L20, 60H10, 60F15, 60F05.
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