Year: 2006
Type: preprint
Abstract: We show that for a quantum $L^p$-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 $L^p$-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.
Source: arXiv (Cornell University)
Author: Luczak, Andrzej
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2143873055