Martingale-type processes indexed by the real line

Details Martingale-type processes indexed by the real line Martingale-type processes indexed by the real line

2010-05-02

arxiv.org/abs/1005.0150v1

Mathematics

Probability

Scientific paper

Some classes of increment martingales, and the corresponding localized classes, are studied. An increment martingale is indexed by the real line and its increment processes are martingales. We focus primarily on the behavior as time goes to minus infinity in relation to the quadratic variation or the predictable quadratic variation, and we relate the limiting behavior to the martingale property. Finally, integration with respect to an increment martingale is studied.

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