Elements of stochastic analysis for the case of Grassmann variables. I. Grassmann stochastic integrals and random processes
Teoretičeskaâ i matematičeskaâ fizika, Tome 96 (1993) no. 1, pp. 23-36 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper is the first part of a study of an approach to the definition of analogs of the concepts of classical stochastic analysis such as a stochastic integral, a random process, a stochastic differential equation, etc., for the case of Grassmann variables in a certain particular situation. Analogs of stochastic integrals and random processes are studied in the first part.
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V. V. Shcherbakov. Elements of stochastic analysis for the case of Grassmann variables. I. Grassmann stochastic integrals and random processes. Teoretičeskaâ i matematičeskaâ fizika, Tome 96 (1993) no. 1, pp. 23-36. http://geodesic.mathdoc.fr/item/TMF_1993_96_1_a1/

[1] Ignatyuk I., Malyshev V., Sidoravichyus V., “Skhodimost metoda stokhasticheskogo kvantovaniya”, Teor. ver. i ee primen., 37:4 (1992) | MR

[2] Parisi G. , Yong-Shi Wu., “Perturbation theory without gauge fixing”, Sci. Sin., 24:4 (1981), 1181–1207 | MR

[3] Migdal A. B., “Stokhasticheskoe kvantovanie v teorii polya”, UFN, 149:1 (1986), 3–44 | DOI | MR

[4] Frohlich J., Ostervalder K., “Is there a euclidean field theory for fermions?”, Helv. Phys. Acta., 47 (1974), 28 | MR

[5] Glimm Dzh., Dzhaffe A., Matematicheskie metody kvantovoi fiziki. Podkhod s tochki zreniya kontinualnykh integralov, Mir, M., 1984 | MR | Zbl

[6] Proceedings of the 1st World Congress of the Bernoulli Society, vol. 1. Probability Theory and Applications (Tashkent 1986), VNU Science Press, Utrecht, 1988 | MR

[7] Quantum probability and applications to the quantum theory of irreversible processes. Proceedings (Villa Mondragone, 1982), Lect. Notes Math., 1055, 1984 | Zbl

[8] Quantum probability and applications. II. Proceedings of the Second Workshop on Quantum Probability and Applications held in Heidelberg (Germany, october 1–5, 1984), Lect. Notes Math., 1136, 1985 | Zbl

[9] Quantum probability and applications. III. Proceedings (Oberwolfach, 1987), Lect. Notes Math., 1303, 1988 | Zbl

[10] Quantum probability and applications. IV. Proceedings (Heidelberg, 1988), Lect. Notes Math., 1396, 1989 | Zbl

[11] Quantum probability and applications. V. Proceedings (Heidelberg, 1988), Lect. Notes Math., 1442 | Zbl

[12] Akkardi L., Fridzherio A., Lyuis D. T., “Kvantovye sluchainye protsessy”, Kvantovye sluchainye protsessy i otkrytye sistemy. Novoe v zarubezhnoi nauke, Mir, M., 1988

[13] Kholevo A. S., Veroyatnostnye i statisticheskie aspekty kvantovoi teorii, Nauka, M., 1988 | MR

[14] Kholevo A. S., “Kvantovoe stokhasticheskoe ischislenie”, Itogi nauki i tekhniki. Sovrem. probl. matematiki. Noveishie dostizheniya, 36, VINITI, 1989, 3–28 | MR

[15] Kholevo A. S., “Uslovno polozhitelno opredelennye funktsii v kvantovoi teorii veroyatnostei”, Itogi nauki i tekhniki. Sovrem, probl. matematiki. Noveishie dostizheniya, 36, VINITI, 1989, 108–148

[16] Belavkin V. P., “Stokhasticheskoe ischislenie kvantovykh vkhodnykh-vykhodnykh protsessov i kvantovaya nerazrushayuschaya filtratsiya”, Itogi nauki i tekhniki. Sovrem. probl. matematiki. Noveishie dostizheniya, 36, VINITI, 1989, 29–68 | MR

[17] Belavkin V. P., “Teorema rekonstruktsii dlya kvantovogo sluchainogo protsessa”, TMF, 62:3 (1985), 409–431 | MR

[18] Barnett C., Streater R. F., Widle I. F., “The Ito–Clifford untegral”, J. Funct. Anal., 48:2 (1982), 172–212 | DOI | MR | Zbl

[19] Malyshev V. A., Minlos R. A., Gibbsovskie sluchainye polya, Nauka, M., 1985 | MR

[20] Doering C. R., “Nonlinear parabolic stochastic differential equations with additive colored noise on $R^d\times R_+$: a regulated stochastic quantization”, Commun. Math. Phys., 109 (1987), 537–561 | DOI | MR | Zbl

[21] Leites D. A., “Vvedenie v teoriyu supermnogoobrazii”, UMN, 35:1 (1980), 3–57 | MR | Zbl

[22] Robertson A., Robertson V., Topologicheskie vektornye prostranstva, Mir, M., 1967 | MR | Zbl