Quantum Stochastic Integrals and Doob-meyer Decomposition
نویسنده
چکیده
Abstract. We show that for a quantum L-martingale (X(t)), p > 2, there exists a Doob-Meyer decomposition of the submartingale (|X(t)|). A noncommutative counterpart of a classical process continuous with probability one is introduced, and a quantum stochastic integral of such a process with respect to an L-martingale, p > 2, is constructed. Using this construction, the uniqueness of the Doob-Meyer decomposition for a quantum martingale ‘continuous with probability one’ is proved, and explicit forms of this decomposition and the quadratic variation process for such a martingale are obtained.
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