Convolution-type stochastic Volterra equations with additive fractional Brownian motion in Hilbert space
| dc.creator | Caithamer, Peter | |
| dc.creator | Karczewska, Anna | |
| dc.date | 2006-11-27 | |
| dc.date.accessioned | 2026-07-07T07:33:24Z | |
| dc.date.available | 2026-07-07T07:33:24Z | |
| dc.description | We consider convolution-type stochastic Volterra equations with additive Hilbert-valued fractional Brownian motion, $0<H<1$. We find the weak solution to this stochastic Volterra equation, and study its stochastic integral part, the stochastic convolution, which we show to be mean-zero Gaussian. We develop an Itô isometry for stochastic integrals with respect to a Hilbert-valued fractional Brownian motion, and use it to compute the covariance of the stochastic convolution. This formula, which uses fractional integrals and derivatives, generalizes the well-known formula from the case $H=1/2$. | |
| dc.description | 12 pages | |
| dc.identifier | https://arxiv.org/abs/math/0611832 | |
| dc.identifier | http://arxiv.org/abs/math/0611832 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/119442 | |
| dc.subject | Probability | |
| dc.subject | 60H20; 45D05; 60H05; 60G15 | |
| dc.title | Convolution-type stochastic Volterra equations with additive fractional Brownian motion in Hilbert space | |
| dc.type | text |