×

Noncommutative stochastic processes with independent and stationary increments satisfy quantum stochastic differential equations. (English) Zbl 0685.60070

See the preview in Zbl 0668.60058.

MSC:

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

Citations:

Zbl 0668.60058
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Abe, E., Hopf algebras (1980), Cambridge: Cambridge University Press, Cambridge · Zbl 0476.16008
[2] Accardi, L.; Frigerio, A.; Lewis, J. T., Quantum stochastic processes, Publ. RIMS Kyoto Univ., 18, 97-133 (1982) · Zbl 0498.60099
[3] Accardi, L.; Schürmann, M.; Waldenfels, W. v., Quantum independent increment processes on superalgebras, Math. Z., 198, 451-477 (1988) · Zbl 0627.60014
[4] Glockner, P., Waldenfels, W. v.: The relations of the non-commutative coefficient algebra of the unitary group. SFB-Preprint Nr. 460, Heidelberg 1988 · Zbl 0812.46070
[5] Guichardet, A., Symmetric Hilbert spaces and related topics (1972), Berlin Heidelberg New York: Springer, Berlin Heidelberg New York · Zbl 0265.43008
[6] Heyer, H., Probability measures on locally compact groups (1977), Berlin Heidelberg New York: Springer, Berlin Heidelberg New York · Zbl 0373.60011
[7] Hochschild, G., On the cohomology groups of an associative algebra, Ann. Math., 46, 58-67 (1945) · Zbl 0063.02029
[8] Hudson, R. L.; Parthasarathy, K. R., Quantum Ito’s formula and stochastic evolutions, Commun. Math. Phys., 93, 301-323 (1984) · Zbl 0546.60058
[9] Hudson, R. L.; Lindsay, J. M., On characterising quantum stochastic evolutions, Math. Proc. Camb. Philos. Soc., 102, 363-369 (1987) · Zbl 0644.46046
[10] Parthasarathy, K. R.; Schmidt, K., Positive definite kernels, continuous tensor products, and central limit theorems of probability theory (1972), Berlin Heidelber New York: Springer, Berlin Heidelber New York · Zbl 0237.43005
[11] Schürmann, M.; Accardi, L.; Waldenfels, W. v., Positive and conditionally positive linear functionals on coalgebras, Quantum Probability and Applications II. Proceedings, Heidelberg 1984 (1985), Berlin Heidelberg New York: Springer, Berlin Heidelberg New York · Zbl 0581.16007
[12] Schürmann, M.: Über^*-Bialgebren und quantenstochastische Zuwachsprozesse. Heidelberg: Dissertation 1985 · Zbl 0624.60012
[13] Sweedler, M. E., Hopf algebras (1969), New York: Benjamin, New York · Zbl 0194.32901
[14] Waldenfels, W. v.; Accardi, L.; Frigerio, A.; Gorini, V., Ito solution of the linear quantum stochastic differential equation describing light emission and absorption, Quantum probability and applications to the theory of irreversible processes. Proceedings, Villa Mondragone 1982 (1984), Berlin Heidelberg New York: Springer, Berlin Heidelberg New York · Zbl 0532.60055
[15] Zink, F.: Generatoren quantenstochastischer Prozesse. Heidelberg: Diplomarbeit 1988
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.