5 papers · 1 filter
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…
Multiparameter Lévy white noise theory and applications
Olfa Draouil, Rahma Yasmina Moulay Hachemi, Bernt Øksendal
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 stochastic heat inclusion with fractional time driven by time-space Brownian and Lévy white noise
Olfa Draouil, Rahma Yasmina Moulay Hachemi, Bernt Øksendal
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 deriva…
The time-fractional heat equation driven by fractional time-space white noise
Rahma Yasmina Moulay Hachemi, Bernt Øksendal
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…
The time-fractional stochastic heat equation driven by time-space white noise
Rahma Yasmina Moulay Hachemi, Bernt Øksendal
We study the time-fractional stochastic heat equation driven by time-space white noise with space dimension and the fractional time-derivative is the C…