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Semi-parametric estimation for forward-backward stochastic differential equations. (English) Zbl 1173.62061
Summary: We suggest a semi-parametric estimation for forward-backward stochastic differential equations (FBSDE) with a linear generator. Both nonparametric and parametric estimators are computationally feasible and the asymptotic properties are standard in the sense of normality. Although there is a plug-in nonparametric estimator in parametric estimation, the high order kernel, under-smoothing and bias correction are not required. Some simulation studies are also given to illustrate our methods.
MSC:
62M05Markov processes: estimation
62F12Asymptotic properties of parametric estimators
62G08Nonparametric regression
62G20Nonparametric asymptotic efficiency
65C60Computational problems in statistics