Geodesic
Martingales in hyperfinite universum
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 2 (2009), pp. 55-66 Cet article a éte moissonné depuis la source Math-Net.Ru

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In article the approach to the theory of the martingales from positions of the non-standard analysis is considered. Definitions are entered and some important results of this theory with proofs are resulted, the part of the stated material belongs to the author. The applications of martingales are resulted in the theory of stochastic integration.
Keywords: Hyperfinite probability space, stochastic process, nonanticipating stochastic process, stochastic integral.
Mots-clés : internal filtration, martingale 
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E. A. Pchelintsev. Martingales in hyperfinite universum. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 2 (2009), pp. 55-66. http://geodesic.mathdoc.fr/item/VTGU_2009_2_a6/

[1] Albeverio S., Fenstad I., Kheeg-Kron R., Lindstrem T., Nestandartnye metody v stokhasticheskom analize i matematicheskoi fizike, Mir, M., 1990, 616 pp.

[2] Martin Väth, Nonstandard analysis, Birkhäuser Verlag, Basel–Boston–Berlin, 2007, 252 pp. | MR

[3] Imme Van den Berg, Victor Neves, The strength of nonstandard analysis, Springer-Verlag, Wien, 2007, 400 pp. | MR

[4] Bulinskii A.V., Shiryaev A.N., Teoriya sluchainykh protsessov, Fizmatlit, M., 2005, 402 pp.

[5] Neve Zh., Matematicheskie osnovy teorii veroyatnostei, Mir, M., 1969, 309 pp.

[6] Liptser R.Sh., Shiryaev A.N., Teoriya martingalov, Nauka, M., 1986, 512 pp.

[7] Robinson A., Nonstandard analysis, Princeton University Press, Princeton, 1996, 293 pp. | MR | Zbl

[8] Devis M., Prikladnoi nestandartnyi analiz, Mir, M., 1980, 234 pp.

[9] Loeb P.A., “Conversion from nonstandard to standard measure spaces and applications in probability theory”, Trans. Amer. Math. Soc., 211 (1975), 113–122 | DOI | MR | Zbl

[10] Luxemburg W.A.J., Nonstandard analysis, Lectures on Robinson's Theory of Infinitesimals and infinitely Large Numbers (Pasadena, 1962), Revised edition, Pasadena, 1964

[11] Machover M., Hirschfeld J., Lectures on nonstandard analysis, Lecture Notes in Mathematics, 94, Springer, Berlin, 1969 | MR | Zbl

[12] Cutland N.J., “Nonstandard measure theory and its applications”, Bull. London Math. Soc., 15, Part 6:57 (1983), 529–589 | DOI | MR | Zbl