Solution space characterisation of perturbed linear discrete and continuous stochastic Volterra convolution equations: the $\ell^p$ and $L^p$ cases
| Autor: | Appleby, John A. D., Lawless, Emmet |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | In this article we are concerned with characterising when solutions of perturbed linear stochastic Volterra summation equations are $p$-summable along with when their continuous time counterparts, perturbed linear stochastic Volterra integrodifferential equations are $p$-integrable. In the discrete case we find it necessary and sufficient that perturbing functions are $p$-summable in order to ensure paths of the discrete equation are $p$-summable almost surely, while in the continuous case it transpires one can have almost surely $p$-integrable sample paths even with non-integrable perturbation functions. For the continuous equation the main converse is clinched by considering an appropriate discretisation and applying results from the discrete case. Comment: 24 pages |
| Databáze: | arXiv |
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