An Optimal Gauss-Markov Approximation for a Process with Stochastic Drift and Applications

Giacomo Ascione; Giuseppe D'Onofrio; Lubomir Kostal; Enrica Pirozzi

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arXiv · 1902.09488

An Optimal Gauss-Markov Approximation for a Process with Stochastic Drift and Applications

Giacomo Ascione·Giuseppe D'Onofrio·Lubomir Kostal·Enrica Pirozzi

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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.

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Giacomo Ascione, Giuseppe D'Onofrio, Lubomir Kostal, Enrica Pirozzi. 2019-02-25. An Optimal Gauss-Markov Approximation for a Process with Stochastic Drift and Applications. https://arxiv.org/abs/1902.09488

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