On Skorohod spaces as universal sample path spaces
| dc.creator | Delzeith, Oliver | |
| dc.date | 2004-12-06 | |
| dc.date.accessioned | 2026-07-07T05:14:57Z | |
| dc.date.available | 2026-07-07T05:14:57Z | |
| dc.description | 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 $ξ$ 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 $ξ$ 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. | |
| dc.description | 15 pages; submitted | |
| dc.identifier | https://arxiv.org/abs/math/0412092 | |
| dc.identifier | http://arxiv.org/abs/math/0412092 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73482 | |
| dc.subject | Probability | |
| dc.subject | Optimization and Control | |
| dc.subject | 60G07 (Primary) 60A10 (Secondary) | |
| dc.title | On Skorohod spaces as universal sample path spaces | |
| dc.type | text |