Weak predictable processes in finite von Neumann algebras

• Autorzy: Mohammed A.
• Języki publikacji: EN

Abstrakty

EN

We investigate the predictable processes as a strong limit of a sequence of simple processes and their stochastic integrals as L2-limit of stochastic integrals of a sequence of simple processes. In the second case new class of predictable processes is defined and characterized, the mutual relations between the von Neumann algebras generated by the various classes of predictable processes are examined.

Słowa kluczowe

EN

Neumann algebras; noncommutative stochastic integration; predictable processes; random times; time projections; martingals

PL

algebra Neumanna; całkowanie stochastyczne; procesy przewidywalne; czas rzutowania; martyngał

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2006
• Tom: Vol. 39, nr 3
• Strony: 553--570
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Mohammed A.

• Department of Mathematics, College of Sciences, Baghdad University, Baghdad, Al-Jadriah, Iraq,

Bibliografia

• [1] C. Barnett, B. Thakrar, Time projection in a von Neumann algebra, J. Operator Theory 18 (1987), 19-31.
• [2] C. Barnett, B. Thakrar, A non-commutative random stopping theorem, J. Funct. Anal. 88 (1990), 342-350.
• [3] C. Barnett, I. F. Wild, Random times and time projections, Proc. Amer. Math. Soc. 110 (1990), 425-440.
• [4] C. Barnett, I. F. Wild, Random times, predictable processes, and stochastic integration in finite von Neumann algebras, Proc. London Math. Soc. (3) 67 (1993), 355-383.
• [5] C. Barnett, R. F. Streater and I. F. Wilde, Quasi-free quantum stochastic integrations for CAR and CCR, J. Funct. Anal 52 (1983), 19-47.
• [6] C. Barnett, V. Camillo, Stopping and projection of non-adapted processes, Soochow J.Math. 23 (2) (1997), 187-212.
• [7] C. Barnett, T. Lyons, Stopping non-commutative processes, Mat. Proc. Comb. Phil. Soc. 99 (1986), 151-161.
• [8] C. Barnett, S. Voliotis, Stopping and integration in a product structure, J. Operator Theory 34 (1995), 145-175.
• [9] A. A. A. Mohammed, Stochastic integration in finite von Neumann algebras, Ph.D. Thesis, Faculty of Mathematics, Lodz University, 2000.
• [10] A. A. A. Mohammed, Stopping and stochastic integrals as closable operators, Probab. Math. Statist. 22, 1 (2002), 167-180.
• [11] A. A. A. Mohammed, On the order structure of time projection, J. Appl. Anal., Vol. 8, No. 2 (2002), pp. 279-95.
• [12] J. R. Ringrose, R. V. Kadison, Fundamentals of The Theory of Operator Algebras, Academic Press, New York-London, 1983.
• [13] M. Takesaki, Theory of Operator Algebras I, Springer-Verlag, New York-Berlin-Heidelberg, 1979.
• [14] F. J. Yeadon, Non-commutative Lp-spaces, Math. Proc. Cambridge Phil. Soc. 77 (1975), 91-102.