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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Basic affine jump diffusion ： ウィキペディア英語版 Basic affine jump diffusion In probability theory, a basic affine jump diffusion (basic AJD) is a stochastic process Z of the form :$dZ\_t=\backslash kappa\; (\backslash theta\; -Z\_t)\backslash ,dt+\backslash sigma\; \backslash sqrt\backslash ,dB\_t+dJ\_t,\backslash qquad\; t\backslash geq\; 0,$ Z_\geq 0, where $B$ is a standard Brownian motion, and $J$ is an independent compound Poisson process with constant jump intensity $l$ and independent exponentially distributed jumps with mean $\backslash mu$. For the process to be well defined, it is necessary that $\backslash kappa\; \backslash theta\; \backslash geq\; 0$ and $\backslash mu\; \backslash geq\; 0$. A basic AJD is a special case of an affine process and of a jump diffusion. On the other hand, the Cox–Ingersoll–Ross (CIR) process is a special case of a basic AJD. Basic AJDs are attractive for modeling default times in credit risk applications,〔〔〔〔 since both the moment generating function :$m\backslash left(\; q\backslash right)\; =\backslash operatorname\; \backslash left(\; e^\backslash right)$ ,\qquad q\in \mathbb, and the characteristic function :$\backslash varphi\; \backslash left(\; u\backslash right)\; =\backslash operatorname\; \backslash left(\; e^\backslash right)\; ,\backslash qquad\; u\backslash in\; \backslash mathbb,$ are known in closed form. The characteristic function allows one to calculate the density of an integrated basic AJD :$\backslash int\_0^t\; Z\_s\; \backslash ,\; ds$ by Fourier inversion, which can be done efficiently using the FFT. ==References== 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Basic affine jump diffusion」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.