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Stochastic serotonin model with discontinuous drift

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  • Milošević, Marija

Abstract

In this paper, motivated by the significance of serotonin in many areas of science, such as biology, neurology, psychiatry, among others, a mathematical serotonin model is proposed. This model incorporates deterministic as well as random influences on the serotonin dynamics. Because of that, the model is based on a system of stochastic differential equations with discontinuous drift coefficient. The main result of the paper is the existence and uniqueness of the solution of that system and due to the nature of the drift coefficient it requires nonstandard approach.

Suggested Citation

  • Milošević, Marija, 2022. "Stochastic serotonin model with discontinuous drift," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 359-374.
    • Handle: RePEc:eee:matcom:v:198:y:2022:i:c:p:359-374
    DOI: 10.1016/j.matcom.2022.03.001
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    References listed on IDEAS

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    1. Eran Lottem & Dhruba Banerjee & Pietro Vertechi & Dario Sarra & Matthijs oude Lohuis & Zachary F. Mainen, 2018. "Activation of serotonin neurons promotes active persistence in a probabilistic foraging task," Nature Communications, Nature, vol. 9(1), pages 1-12, December.
    2. Nikolaos Halidias & P. E. Kloeden, 2006. "A note on strong solutions of stochastic differential equations with a discontinuous drift coefficient," International Journal of Stochastic Analysis, Hindawi, vol. 2006, pages 1-6, May.
    3. Przybyłowicz, Paweł & Szölgyenyi, Michaela & Xu, Fanhui, 2021. "Existence and uniqueness of solutions of SDEs with discontinuous drift and finite activity jumps," Statistics & Probability Letters, Elsevier, vol. 174(C).
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