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- W2490932324 abstract "The following random recurrency: $$ W_{n+1} = U_{n+1} ( W_n + Lambda_{n+1} ) $$ where $W_{-1}=0.$ is known to be associated with the shot noise : $$ W_{t} = sum_{0<t_k<t} Lambda_{k} e^{-(t-t_k)} $$ where the $t_k$ are the dates of a Poisson process, the $ U_i ; i = 0,1,... $ are independent uniform variables. This can be extended to the triggered shot noise : $$ W_{t} = sum_{0<t_{lk}<t} Lambda_{lk} e^{-(t-t_{lk})} , l=1,2,3,... $$ The random amplitudes $Lambda_i, i = 0,1,... $ are positive Dufresne independent variables or also even density variables which characteristic function given by generalized hypergeometric function. Keywords: Random Difference Equations,Triggered Shot Noise, Iterated Cosine-Bessel functions, Logarithmic Distribution Functions,Saddle Point Method, Asymptotic Calculations, Generalized Hypergeometric Functions, Psi Functions." @default.
- W2490932324 created "2016-08-23" @default.
- W2490932324 creator A5076439619 @default.
- W2490932324 date "2013-12-04" @default.
- W2490932324 modified "2023-09-27" @default.
- W2490932324 title "Computational Tools for the Shot Noise with Random Amplitude" @default.
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