Marinelli, Carlo;
Scarpa, Luca;
(2022)
On the Positivity of Local Mild Solutions to Stochastic Evolution Equations.
In: Ugolini, S and Fuhrman, M and Mastrogiacomo, E and Morando, P and Rüdiger, B, (eds.)
Springer Proceedings in Mathematics and Statistics.
(pp. pp. 231-245).
Springer International Publishing: Cham, Switzerland.
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Abstract
We provide sufficient conditions on the coefficients of a stochastic evolution equation on a Hilbert space of functions driven by a cylindrical Wiener process ensuring that its mild solution is positive if the initial datum is positive. As an application, we discuss the positivity of forward rates in the Heath-Jarrow-Morton model via Musiela’s stochastic PDE.
| Type: | Proceedings paper |
|---|---|
| Title: | On the Positivity of Local Mild Solutions to Stochastic Evolution Equations |
| Event: | Geometry and Invariance in Stochastic Dynamics RTISD19 2019 |
| ISBN-13: | 9783030874315 |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/978-3-030-87432-2_12 |
| Publisher version: | https://doi.org/10.1007/978-3-030-87432-2_12 |
| Language: | English |
| Additional information: | This version is the author-accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Positivity, Mild solutions, Stochastic evolution equations, HJM model. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10189730 |
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