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

Giacomo Ascione, D’Onofrio, Giuseppe, Lubomir Kostal and Enrica Pirozzi

Stochastic Processes and their Applications, 2020, vol. 130, issue 11, 6481-6514

Abstract: 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.

Keywords: Stochastic differential equations; Optimality conditions; Shot noise; Neuronal models (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:130:y:2020:i:11:p:6481-6514

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DOI: 10.1016/j.spa.2020.05.018

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