Sankhya: The Indian Journal of Statistics

1998, Volume 60, Series A, Pt. 1 ,pp. 57-73

UNIFORM APPROXIMATION FOR FAMILIES OF STOCHASTIC INTEGRALS

By

B.L.S. PRAKASA RAO, Indian Statistical Institute, New Delhi

SUMMARY. Uniform approximations for families of stochastic integrals of Rubin-Fisk-Stratonovich type and Ito type are studied. It is shown that the approximants of Rubin-Fisk-Stratonovich type obtained from partitions of equal size converge faster to the corresponding stochastic integral than the approximants of Ito type for such partitions converge to the corresponding stochastic integral. Methods used for the study of families of stochastic integrals are of independent interest.

AMS (1991) subject classification. Primary 60H05.

Key words and phrases. Approximation of stochastic integral; Rubin-Fisk-Stratonovich integral; Ito integral; stochastic analysis.

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