Quantum stochatic integrals and Doob-Meyer decomposition

الأصل · EN

We show that for a quantum Lᵖ-martingale (X(t)), p>2, there exists a Doob-Meyer decomposition of the submartingale (|X(t)|²). 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 Lᵖ-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.