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

Author

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

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.

Suggested Citation

  • Ascione, Giacomo & D’Onofrio, Giuseppe & Kostal, Lubomir & Pirozzi, Enrica, 2020. "An optimal Gauss–Markov approximation for a process with stochastic drift and applications," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 6481-6514.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:11:p:6481-6514
    DOI: 10.1016/j.spa.2020.05.018
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    References listed on IDEAS

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    1. Aniello Buonocore & Luigia Caputo & Enrica Pirozzi & Luigi M. Ricciardi, 2011. "The First Passage Time Problem for Gauss-Diffusion Processes: Algorithmic Approaches and Applications to LIF Neuronal Model," Methodology and Computing in Applied Probability, Springer, vol. 13(1), pages 29-57, March.
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