Quadratic variation of a stochastic process and its application.

Source

Proceedings of the 1970 international symposium on information theory. IEEE. 1970, pp.1 pp.. New York, NY, USA.

Date of Publication

1970

Country of Publication

USA.

Conference Information

Noordwijk, Netherlands. IEEE, Information theory group. Union Radio Scientifique Internationale. US Air Force Office Sci. Res. 15-19 June 1970.

Abstract

Abstract only given, substantially as follows. The natural context in which quadratic variation should be examined is in connection with sample continuous second order martingales. It can be shown that every such martingale has a non-zero quadratic variation unless it is a fixed random variable independent of time. Now consider a process which is the sum of a sample continuous second order martingale and a sample continuous process with sample functions which are almost surely of bounded variation. Because sample continuity and bounded variation together imply zero bounded variation, the quadratic variation of the sum must be due entirely to the martingale term. This has some interesting and surprising consequences which are explored.