**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 X_{t }such that the conditional expectation of X_{t }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.