Sankhya: The Indian Journal of Statistics

1995, Volume 57, Series A, Pt. 1, pp. 11--28

STATISTICAL INFERENCE FOR SWITCHING BROWNIAN MOTION

By

HALINA FRYDMAN and TAUKIR HUSSAIN, New York University

SUMMARY.  A notion of switching Brownian Motion (SWBM) process induced by a diffusion process is introduced. This notion arose in the context of finding an approximate method of estimation of diffusion parameters from a new random sampling scheme. However, SWBM processes are considered here as a model of interest in their own right. The general method of estimation for the parameters of SWBM processes induced by the specified class of diffusion processes is proposed and asymptotic inference is developed for the parameters of some SWBM processes.

AMS (1990) subject classification.  62M05, 60J60, 60J65.

Key words and phrases. Diffusion processes, random sampling scheme, switching Brownian motions.

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