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We consider inference of the parameters of the diffusion term forCox-Ingersoll-Ross and similar processes with a power type dependence of thediffusion coefficient from the underlying process. We suggest some originalpathwise estimates for this coefficient and for the power index based on ananalysis of an auxiliary continuous time complex valued process generated bythe underlying real valued process. These estimates do not rely on thedistribution of the underlying process and on a particular choice of the drift.Some numerical experiments are used to illustrate the feasibility of thesuggested method.

A pathwise inference method for the parameters of diffusion terms