4 papers
A time-fractional Kalman filter
Olfa Draouil, Rahma Yasmina Moulay Hachemi, Bernt Øksendal +1
We study a linear filtering problem in which the signal process is described by a time-fractional linear stochastic differential equation driven by Brownian motion. We derive a sto…
The stochastic heat inclusion with fractional time driven by time-space Brownian and Lévy white noise
Olfa Draouil, Rahma Yasmina Moulay Hachemi, Bernt Ãksendal
We study a time-fractional stochastic heat inclusion driven by additive time-space Brownian and Lévy white noise. The fractional time derivative is interpreted as the Caputo deriv…
Multiparameter Lévy white noise theory and applications
Olfa Draouil, Rahma Yasmina Moulay Hachemi, Bernt Ãksendal
We construct a white noise theory and white noise calculus for the (multi-parameter) L\' evy sheet and its compensated Poisson random measures. The theory applies to stochastic par…
The time-fractional heat equation driven by fractional time-space white noise
Rahma Yasmina Moulay Hachemi, Bernt Ãksendal
We give an introduction to the time-fractional stochastic heat equation driven by 1+d-parameter fractional time-space white noise, in the following two cases: (i) With additive noi…