An optimal Gauss-Markov approximation for a process with stochastic drift and applications

0534260 - FGÚ 2021 RIV NL eng J - Článek v odborném periodiku
Ascione, G. - D´Onofrio, G. - Košťál, Lubomír - Pirozzi, E.
An optimal Gauss-Markov approximation for a process with stochastic drift and applications.
Stochastic Processes and their Applications. Roč. 130, č. 11 (2020), s. 6481-6514. ISSN 0304-4149. E-ISSN 1879-209X
Grant CEP: GA ČR(CZ) GA20-10251S
Institucionální podpora: RVO:67985823
Klíčová slova: stochastic differential equations * optimality conditions * shot noise * neuronal models
Obor OECD: Statistics and probability
Impakt faktor: 1.467, rok: 2020
Způsob publikování: Omezený přístup
https://doi.org/10.1016/j.spa.2020.05.018

We consider a linear stochastic differential equation with stochastic drift. We study the problem of approximating the solution of such equation through an Ornstein–Uhlenbeck type process, by using direct methods of calculus of variations. We show that general power cost functionals satisfy the conditions for existence and uniqueness of the approximation. We provide some examples of general interest and we give bounds on the goodness of the corresponding approximations. Finally, we focus on a model of a neuron embedded in a simple network and we study the approximation of its activity, by exploiting the aforementioned results.
Trvalý link: http://hdl.handle.net/11104/0312486