Sankhya: The Indian Journal of Statistics

1996, Volume 58, Series A, Pt. 3, pp. 382--391

GAUSSIAN PROCESSES AND LINEAR INTERPOLATION

By

MILAN MERKLE, University of Belgrade

and

LJILJANA PETROVI\'C, University of Kragujevac

SUMMARY.  We study Gaussian processes Xt such that the conditional expectation of Xt given values of X in a finite set S is a linear interpolation between two nearest values. For processes with independent increments, a characterization in terms of covariance function is given, together with a characterization of Weiner process. Using the theory of reciprocal processes, we give a characterization of Markov processes with linear interpolation property.

AMS (1992) subject classification.  Primary 60G12, 60G15.

Key words and phrases. Gaussian processes, reciprocal processes, linear interpolation.

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