Geodesic
Probability density function of leaky integrate-and-fire model with L\'evy noise and its numerical approximation
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 19 (2016) no. 1, pp. 87-96

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We investigate a numerical analysis of a leaky integrate-and-fire model with Lévy noise. We consider a neuron model in which the probability density function of a neuron in some potential at any time is modeled by a transport equation. Lévy noise is included due to jumps by excitatory and inhibitory impulses. Due to these jumps the resulting equation is a transport equation containing two integrals in the right-hand side (jumps). We design, implement, and analyze numerical methods of finite volume type. Some numerical examples are also included. 
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     author = {P. Singh and M. K. Kadalbajoo and K. Sharma},
     title = {Probability density function of leaky integrate-and-fire model with {L\'evy} noise and its numerical approximation},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
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P. Singh; M. K. Kadalbajoo; K. Sharma. Probability density function of leaky integrate-and-fire model with L\'evy noise and its numerical approximation. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 19 (2016) no. 1, pp. 87-96. http://geodesic.mathdoc.fr/item/SJVM_2016_19_1_a8/