Abstract
AbstractConsider a continuous local martingale X. We say that X satisfies the representation property if any martingale Y of X can be represented as stochastic ITǑ integral of X. Using the method of random time change systematically, in the present paper the representation problem for continuous local martingales is treated. We describe a class of martingales Y that can be represented as stochastic integral of X by probabilistic conditions. This leads to sufficient conditions for the representation property of X being true. Besides, an interesting characterization of continuous processes with independent increments is obtained. In part II. we proceed with general examples, applications to the n‐dimensional case, and, in particular, to the n‐dimensional time change of continuous local martingales with orthogonal components.
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