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Spectral methods for identifying scalar diffusions. (English) Zbl 0962.62094
Summary: This paper shows how to identify nonparametrically scalar stationary diffusions from discrete-time data. The local evolution of the diffusion is characterized by a drift and diffusion coefficient along with the specification of boundary behavior. We recover this local evolution from two objects that can be inferred directly from discrete-time data: the stationary density and a conveniently chosen eigenvalue-eigenfunction pair of the conditional expectation operator over a unit interval of time. This construction also lends itself to a spectral characterization of the over-identifying restrictions implied by a scalar diffusion model of a discrete-time Markov process.

62M99 Inference from stochastic processes
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
62G99 Nonparametric inference
62P05 Applications of statistics to actuarial sciences and financial mathematics
47N30 Applications of operator theory in probability theory and statistics
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