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Random partition and stochastic integration in finite von Neumann algebras

Mohammed A. A. A.

Journal of Applied Analysis

2007

Vol. 13, nr 1

33-56

We introduce the notion of a random partition of the stochastic interval [τ 0, τ ∞] as an analogy to the classical case and characterize the predictable processes associated with such partitions. Also we identify the operator algebras connected with the stochastic integrals of predictable processes and examine their mutual relations.

Weak predictable processes in finite von Neumann algebras

Mohammed A.

Demonstratio Mathematica

2006

Vol. 39, nr 3

553-570

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.