Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.13791 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- The classic stochastic Fubini theorem says that if one stochastically integrates with respect to a semimartingale $S$ an $η(dz)$-mixture of $z$-parametrized integrands $ψ^z$, the result is just the $η(dz)$-mixture of the individual $z$-parametrized stochastic integrals $\intψ^z{d}S.$ But if one wants to use such a result for the study of Volterra semimartingales of the form $ X_t =\int_0^t Ψ_{t,s}dS_s, t \geq0,$ the classic assumption that one has a fixed measure $η$ is too restrictive; the mixture over the integrands needs to be taken instead with respect to a stochastic kernel on the parameter space. To handle that situation and prove a corresponding new stochastic Fubini theorem, we introduce a new notion of measure-valued stochastic integration with respect to a general multidimensional semimartingale. As an application, we show how this allows to handle a class of quite general stochastic Volterra semimartingales.