Anticipating integrals and martingales on the Poisson space

Details Anticipating integrals and martingales on the Poisson space Anticipating integrals and martingales on the Poisson space

2005-04-12

arxiv.org/abs/math/0504244v1

Mathematics

Probability

Probability Theory

Scientific paper

Let $\tilde{N}\_{t}$ be a standard compensated Poisson process on $[0,1]$. We prove a new characterization of anticipating integrals of the Skorohod type with respect to $\tilde{N}$, and use it to obtain several counterparts to well established properties of semimartingale stochastic integrals. In particular we show that, if the integrand is sufficiently regular, anticipating Skorohod integral processes with respect to $\tilde{N}$ admit a pointwise representation as usual It\^{o} integrals in an independently enlarged filtration. We apply such a result to: (i) characterize Skorohod integral processes in terms of products of backward and forward Poisson martingales, (ii) develop a new It\^{o}-type calculus for anticipating integrals on the Poisson space, and (iii) write Burkholder-type inequalities for Skorohod integrals.

Affiliated with

Also associated with

No associations

Rating

Anticipating integrals and martingales on the Poisson space 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 Anticipating integrals and martingales on the Poisson space, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Anticipating integrals and martingales on the Poisson space will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-350585