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Barnett, C.; Streater, R. F.; Wilde, I. F.

The Ito-Clifford integral. III: The Markov property of solutions to stochastic differential equations. (English) Zbl 0527.60059

Commun. Math. Phys. 89, 13-17 (1983).
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Cited in 1 Review
Cited in 6 Documents

MSC:

60H05 Stochastic integrals
46L51 Noncommutative measure and integration
46L53 Noncommutative probability and statistics
46L54 Free probability and free operator algebras
60J25 Continuous-time Markov processes on general state spaces

Keywords:

Ito-Clifford stochastic integral; von Neumann algebra

Citations:

Zbl 0492.46051; Zbl 0503.60065
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Full Text: DOI

References:

[1] Accardi, L., Frigerio, A., Lewis, J.: A class of quantum stochastic processes. Preprint · Zbl 0498.60099
[2] Barnett, C., Streater, R. F., Wilde, I. F.: The Itô-Clifford integral. J. Funct. Anal.48, 172-212 (1982) · Zbl 0492.46051 · doi:10.1016/0022-1236(82)90066-0
[3] Barnett, C., Streater, R. F., Wilde, I. F.: Itô-Clifford integral II-stochastic differential equations. J. London Math Soc (to appear) · Zbl 0503.60065
[4] Cockroft, A. M., Hudson, R. L.: Quantum mechanical Wiener processes. J. Multivar. Anal.7, 107-124 (1978) · Zbl 0401.60086 · doi:10.1016/0047-259X(77)90035-5
[5] Davies, E. B.: Quantum theory of open systems. New York: Academic Press 1976 · Zbl 0388.46044
[6] Gross, L.: Existence and uniqueness of physical ground states. J. Funct. Anal.10, 52-109 (1972) · Zbl 0237.47012 · doi:10.1016/0022-1236(72)90057-2
[7] Hudson, R. L., Parthasarathy, K. R.: Quantum diffusions, Proceedings of IFIP-ISI conference on theory and applications of random fields, 1982. In: Lecture Notes in Mathematics. Berlin, Heidelberg, New York: Springer 1982; and preprint
[8] Kunze, R.:L p Fourier transforms on locally compact unimodular groups. Trans. Am. Math. Soc.89, 519-540 (1958) · Zbl 0084.33905
[9] Lindblad, G.: On the generators of quantum dynamical semigroups. Commun. Math. Phys.48, 119-130 (1976) · Zbl 0343.47031 · doi:10.1007/BF01608499
[10] Nelson, E.: The free Markov field. J. Funct. Anal.12, 211-227 (1973) · Zbl 0273.60079 · doi:10.1016/0022-1236(73)90025-6
[11] Schrader, R., Uhlenbrock, D.: Markov structures on Clifford algebras. J. Funct. Anal.18, 369-413 (1975) · Zbl 0337.46062 · doi:10.1016/0022-1236(75)90011-7
[12] Segal, I. E.: A non-commutative extension of abstract integration. Ann. Math.57, 401-457 (1953);58, 595-596 (1953) · Zbl 0051.34201 · doi:10.2307/1969729
[13] Segal, I. E.: Tensor algebras over Hilbert spaces II. Ann. Math.63, 160-175 (1956) · Zbl 0073.09403 · doi:10.2307/1969994
[14] Wilde, I. F.: The free fermion field as a Markov field. J. Funct. Anal.15, 12-21 (1974) · Zbl 0276.60095 · doi:10.1016/0022-1236(74)90022-6
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