# Characterization of unitary processes with independent and stationary increments

Lingaraj Sahu; Kalyan B. Sinha

Annales de l'I.H.P. Probabilités et statistiques (2010)

- Volume: 46, Issue: 2, page 575-593
- ISSN: 0246-0203

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topSahu, Lingaraj, and Sinha, Kalyan B.. "Characterization of unitary processes with independent and stationary increments." Annales de l'I.H.P. Probabilités et statistiques 46.2 (2010): 575-593. <http://eudml.org/doc/240601>.

@article{Sahu2010,

abstract = {This is a continuation of the earlier work (Publ. Res. Inst. Math. Sci.45 (2009) 745–785) to characterize unitary stationary independent increment gaussian processes. The earlier assumption of uniform continuity is replaced by weak continuity and with technical assumptions on the domain of the generator, unitary equivalence of the process to the solution of an appropriate Hudson–Parthasarathy equation is proved.},

author = {Sahu, Lingaraj, Sinha, Kalyan B.},

journal = {Annales de l'I.H.P. Probabilités et statistiques},

keywords = {unitary processes; noise space; Hudson–Parthasarathy equations; quantum stochastic calculus; quantum unitary process with i.i.d. stationary increments; quantum Gaussian process},

language = {eng},

number = {2},

pages = {575-593},

publisher = {Gauthier-Villars},

title = {Characterization of unitary processes with independent and stationary increments},

url = {http://eudml.org/doc/240601},

volume = {46},

year = {2010},

}

TY - JOUR

AU - Sahu, Lingaraj

AU - Sinha, Kalyan B.

TI - Characterization of unitary processes with independent and stationary increments

JO - Annales de l'I.H.P. Probabilités et statistiques

PY - 2010

PB - Gauthier-Villars

VL - 46

IS - 2

SP - 575

EP - 593

AB - This is a continuation of the earlier work (Publ. Res. Inst. Math. Sci.45 (2009) 745–785) to characterize unitary stationary independent increment gaussian processes. The earlier assumption of uniform continuity is replaced by weak continuity and with technical assumptions on the domain of the generator, unitary equivalence of the process to the solution of an appropriate Hudson–Parthasarathy equation is proved.

LA - eng

KW - unitary processes; noise space; Hudson–Parthasarathy equations; quantum stochastic calculus; quantum unitary process with i.i.d. stationary increments; quantum Gaussian process

UR - http://eudml.org/doc/240601

ER -

## References

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- [9] A. Mohari. Quantum stochastic differential equations with unbounded coefficients and dilations of Feller’s minimal solution. Sankhyā Ser. A 53 (1991) 255–287. Zbl0751.60062MR1189771
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- [11] K. R. Parthasarathy. An Introduction to Quantum Stochastic Calculus. Monographs in Mathematics 85. Birkhäuser, Basel, 1992. Zbl0751.60046MR1164866
- [12] L. Sahu, M. Schürmann and K. B. Sinha. Unitary processes with independent increments and representations of Hilbert tensor algebras. Publ. Res. Inst. Math. Sci. 45 (2009) 745–785. Zbl1194.81138MR2569566
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