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J-GLOBAL ID:201802216714126683
Reference number:18A1311713 Asymptotic expansion of a nonlinear oscillator with a jump-diffusion process
ジャンプ拡散過程を有する非線形オシレータの漸近展開
- Applebaum, D.: Lévy Processes and Stochastic Calculus, 2nd edn. Cambridge University Press, Cambridge (2009)
- Benhamou, E., Gobet, E., Miri, M.: Smart expansion and fast calibration for jump diffusion. Finance Stoch. 13, 563-589 (2009)
- Bulsara, A.R., Elston, T.C., Doering, C.R., Lowen, S.B., Lindenberg, K.: Cooperative behavior in periodically driven noisy integrate-fire models of neuronal dynamics. Phys. Rev. E 3(53), 3958-3969 (1996)
- DeFelice, L.J.: Introduction to Membrane Noise. Springer, Berlin (1981)
- Durret, R.: Stochastic Calculus: A Practical Introduction (Probability and Stochastics Series). CRC Press, Boca Rotan (1996)
- Fujiwara, T., Kunita, H.: Stochastic differential equations of jump type and lévy processes in diffeomorphisms group. J. Math. Kyoto Univ. (JMKYAZ) 25(1), 71-106 (1985)
- Gautschi, W.: Orthogonal Polynomials: Computation and Approximation. Oxford University Press, Oxford (2004)
- Gerstein, G.L., Mandelbrot, B.: Random walk models for the spike activity of a single neuron. Biophys. J. 4, 41-68 (1964)
- Giraudo, M.T., Sacerdote, L.: Jump-diffusion processes as models for neuronal activity. Biosystems 40, 75-82 (1997)
- Goldwyn, J.H., Shea-Brown, E.: The what and where of adding channel noise to the Hodgkin-Huxley equations. PLos. Comput. Biol. 7, e1002,247 (2011)
- Griebel, M., Oettershagen, J.: Dimension-adaptive sparse grid quadrature for integrals with boundary singularities. In: Sparse grids and Applications, Lecture Notes in Computational Science and Engineering, vol. 97, pp. 109-136. Springer. Also available as INS Preprint no 1310 (2014)
- Griebel, M., Oettershagen, J.: Dimension-adaptive sparse grid quadrature for integrals with boundary singularities. In: Sparse Grids and Applications, vol. 97, chap, pp. 109-136. Springer (2014)
- Guckenheimer, J.: Isochrons and phasphase sets. J. Math. Biol. 1, 259-273 (1975)
- Hayashi, M., Ishikawa, Y.: Composition with distributions of Wiener-Poisson variables and its asymptotic expansion. Math. Nachr. 285, 619-658 (2012)
- Hohn, N., Burkitt, A.N.: Shot noise in the leaky integrate-and-fire neuron. Phys. Rev. E (3) 63(3 Pt 1), 031902 (2001)
- Ishikawa, Y.: Stochastic Calculus of Variations for Jump Processes, 2nd edn (De Gruyter Studies in Mathematics). Walter De Gruyter GmbH, Berlin (2016)
- Izhikevich, E.M.: Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting. The MIT Press, Cambridge (2010)
- Kandel, E.R., Schwartz, J.H., Jessell, T.M., Siegelbaum, S.A., Hudspeth, A.J.: Principles of Neural Science, 5th edn. The McGraw-Hill companies, Inc., New York (2013)
- Kavalali, E.T.: The mechanisms and functions of spontaneous neurotransmitter release. Nat. Rev. Neurosci. 16, 5-16 (2015)
- Kunita, H.: Nondegenerate SDE’s with jumps and their hypoelliptic properties. J. Math. Soc. Jpn. 65(3), 993-1035 (2013)
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