Mathematics – Probability
Scientific paper
2004-12-06
Mathematics
Probability
15 pages; submitted
Scientific paper
The paper presents a factorization theorem for a certain class of stochastic processes. Skorohod spaces carry the rich structure of standard Borel spaces and appear to be suitable universal sample path spaces. We show that, if $\xi$ is a RCLL stochastic process with values in a complete separable metric space $E$, any other RCLL stochastic process $X$ adapted to the filtration induced by $\xi$ factors through the Skorohod space $D_E[0,\infty)$. This can be understood as an extension of a stochastic process to a standard Borel space enjoying nice properties. Moreover, the trajectories of the factorized stochastic process defined on $D_E[0,\infty)$ inherit the properties of being continuous, non-decreasing, and of bounded variation, resp., from those of $X$. Considering situations which are invariant under the factorization procedure, the main theorem is a reduction tool to assume the underlying measurable space be a standard Borel space. In an example, we pick the existence theorem of regular conditional probabilities on standard Borel spaces to simplify a conditional expectation appearing in stochastic control problems.
No associations
LandOfFree
On Skorohod spaces as universal sample path spaces 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 On Skorohod spaces as universal sample path spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Skorohod spaces as universal sample path spaces will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-41056