Asymptotic expansion of a nonlinear oscillator with a jump-diffusion process

作者：Ishikawa Yasushi; Yamanobe Takanobu^*

来源：Japan Journal of Industrial and Applied Mathematics, 2018, 35(2): 969-1004.

DOI：10.1007/s13160-018-0312-1

• Synaptic noise
• Ion channel noise
• Nonlinear oscillator
• Stuart-Landau oscillator
• Wiener-Poisson space
• Malliavin calculus

We introduce an asymptotic expansion of the transition density of a nonlinear oscillator involving a jump-diffusion process. We approximate the transition density by expanding the characteristic function of the solution to the nonlinear oscillator with respect to time and present a numerical verification of the asymptotic expansion of the transition density. This study provides us with a new mathematical framework for analyzing the dynamics of stochastic mathematical neuronal models using a jump-diffusion process.

• 出版日期2018-7