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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
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[1] Abe, E.: Hopf algebras. Cambridge: Cambridge University Press 1980 · 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 · doi:10.2977/prims/1195184017
[3] Accardi, L., Schürmann, M., Waldenfels, W. v.: Quantum independent increment processes on superalgebras. Math. Z.198, 451-477 (1988) · Zbl 0627.60014 · doi:10.1007/BF01162868
[4] Glockner, P., Waldenfels, W. v.: The relations of the non-commutative coefficient algebra of the unitary group. SFB-Preprint Nr. 460, Heidelberg 1988
[5] Guichardet, A.: Symmetric Hilbert spaces and related topics. (Lect. Notes Math., vol. 261). Berlin Heidelberg New York: Springer 1972 · Zbl 0265.43008
[6] Heyer, H.: Probability measures on locally compact groups. Berlin Heidelberg New York: Springer 1977 · Zbl 0376.60002
[7] Hochschild, G.: On the cohomology groups of an associative algebra. Ann. Math.46, 58-67 (1945) · Zbl 0063.02029 · doi:10.2307/1969145
[8] Hudson, R.L., Parthasarathy, K.R.: Quantum Ito’s formula and stochastic evolutions. Commun. Math. Phys.93, 301-323 (1984) · Zbl 0546.60058 · doi:10.1007/BF01258530
[9] Hudson, R.L., Lindsay, J.M.: On characterising quantum stochastic evolutions. Math. Proc. Camb. Philos. Soc.102, 363-369 (1987) · Zbl 0644.46046 · doi:10.1017/S0305004100067372
[10] Parthasarathy, K.R., Schmidt, K.: Positive definite kernels, continuous tensor products, and central limit theorems of probability theory. (Lect. Notes Math., vol. 272). Berlin Heidelber New York: Springer 1972 · Zbl 0237.43005
[11] Schürmann, M.: Positive and conditionally positive linear functionals on coalgebras. In: Accardi, L., Waldenfels, W. v. (eds.) Quantum Probability and Applications II. Proceedings, Heidelberg 1984. (Lect. Notes Math., vol. 1136). Berlin Heidelberg New York: Springer 1985 · Zbl 0581.16007
[12] Schürmann, M.: Über*-Bialgebren und quantenstochastische Zuwachsprozesse. Heidelberg: Dissertation 1985 · Zbl 0624.60012
[13] Sweedler, M.E.: Hopf algebras. New York: Benjamin 1969 · Zbl 0194.32901
[14] Waldenfels, W. v.: Ito solution of the linear quantum stochastic differential equation describing light emission and absorption. In: Accardi, L., Frigerio, A., Gorini, V. (eds.) Quantum probability and applications to the theory of irreversible processes. Proceedings, Villa Mondragone 1982. (Lect. Notes Math., vol. 1055). Berlin Heidelberg New York: Springer 1984
[15] Zink, F.: Generatoren quantenstochastischer Prozesse. Heidelberg: Diplomarbeit 1988
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