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

0534260 - FGÚ 2021 RIV NL eng J - Journal Article
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
R&D Projects: GA ČR(CZ) GA20-10251S
Institutional support: RVO:67985823
Keywords : stochastic differential equations * optimality conditions * shot noise * neuronal models
OECD category: Statistics and probability
Impact factor: 1.467, year: 2020
Method of publishing: Limited access
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.
Permanent Link: http://hdl.handle.net/11104/0312486