Filtered stochastic calculus

Details Filtered stochastic calculus Filtered stochastic calculus

2001-03-06

arxiv.org/abs/math/0103033v1

Inf. Dim. Anal. Quant. Probab. Rel. Topics, Vol.4 (2001), 309-346

Mathematics

Quantum Algebra

37 pages, latex, no figures, accepted for publication in IDA-QP

Scientific paper

By introducing a color filtration to the multiplicity space, we extend the quantum Ito calculus on multiple symmetric Fock space to the framework of filtered adapted biprocesses. In this new notion of adaptedness,``classical'' time filtration makes the integrands similar to adapted processes, whereas ``quantum'' color filtration produces their deviations from adaptedness. An important feature of this calculus, which we call filtered stochastic calculus, is that it provides an explicit interpolation between the main types of calculi, regardless of the type of independence, including freeness, Boolean independence (more generally, m-freeness) as well as tensor independence. Moreover, it shows how boson calculus is ``deformed'' by other noncommutative notions of independence.

Affiliated with

Also associated with

No associations

Rating

Filtered stochastic calculus does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Filtered stochastic calculus, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Filtered stochastic calculus will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-431546