## Higher order Ito product formula and generators of evolutions and flows.(English)Zbl 0850.81035

Summary: A simple combinatorial formula is found for the product of two iterated quantum stochastic integrals, and used to find conditions that such an integral represent a unitary-valued or $$*$$-algebra homomorphism-valued process.

### MSC:

 81S25 Quantum stochastic calculus 46L60 Applications of selfadjoint operator algebras to physics
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### References:

 [1] Evans, M. P. (1989). Existence of quantum diffusions,Probability Theory and Related Fields,81, 473-483. · Zbl 0667.60060 [2] Hudson, R. L. (1990). Quantum stochastic flows, inProbability Theory and Mathematical Statistics, Vol. 1, B. Grigelioniset al., eds., VSP Utrecht, pp. 512-525. · Zbl 0743.46068 [3] Hudson, R. L., and Parthasarathy, K. R. (1984). Quantum Ito’s formula and stochastic evolutions,Communications in Mathematical Physics,93, 301-323. · Zbl 0546.60058 [4] Hudson, R. L., and Parthasarathy, K. R. (1993). Casimir chaos map for U(N).Tatra Mountains Mathematical Publications,3, 1-9. · Zbl 0798.60068 [5] Parthasarathy, K. R. (1992).An Introduction to Quantum Stochastic Calculus, Birkh?user, Basle. · Zbl 0751.60046
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