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On multi-dimensional Markovian cocycles. (English) Zbl 0674.60064
Quantum probability and applications IV, Proc. Year, Rome/Italy 1987, Lect. Notes Math. 1396, 59-67 (1989).
Summary: [For the entire collection see Zbl 0672.00013.]
Under a weak differentiability condition, quantum Markov cocycles on a Fock space satisfy quantum stochastic differential equations of the form $$dV=VF_{\alpha \beta}d\Lambda^{\alpha \beta}$$ where $$\{F_{\alpha \beta}\}$$ is a matrix of operators with common dense domain, $$\Lambda^{\alpha \beta}$$ are the basic martingales of the Hudson- Parthasarathy calculus in n-dimensions and $$\Lambda^{\infty}$$ is time.

##### MSC:
 60H99 Stochastic analysis 81P20 Stochastic mechanics (including stochastic electrodynamics) 60K35 Interacting random processes; statistical mechanics type models; percolation theory 46L51 Noncommutative measure and integration 46L53 Noncommutative probability and statistics 46L54 Free probability and free operator algebras