A Gaussian-generalized inverse Gaussian finite-dimensional filter

Marco Ferrante and Paolo Vidoni

Stochastic Processes and their Applications, 1999, vol. 84, issue 1, 165-176

Abstract: We consider the filtering problem for a partially observable stochastic process , solution to a nonlinear system of stochastic difference equations, which provides a stochastic modellization for both the mean and the variance of the Gaussian observation distribution. The noises in the equations are given by two sequences of independent Gaussian random variables and a sequence of independent gamma random variables. We are able to prove that there exists a finite-dimensional filter system for this model, since, for each n, the conditional distribution of (Xn,Zn) given (Y0,...,Yn) is that of a suitable bivariate Gaussian-generalized inverse Gaussian random variable.

Keywords: Finite; dimensional; filter; Generalized; hyperbolic; distribution; Generalized; inverse; Gaussian; distribution; Stochastic; filtering; Stochastic; volatility (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (1)

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