Lévy Processes and Stochastic Calculus: Lévy processes
Lévy Processes and Stochastic Calculus: Lévy processes
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DOI：
10.1017/cbo9780511755323.004
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发表时间：
2004
期刊：
影响因子：
--
通讯作者：
David Applebaum
中科院分区：
文献类型：
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作者：
David Applebaum
Levy 过程形成了一类广泛而丰富的随机过程，并且具有从物理到金融的许多应用。随机微积分是与随机噪声相互作用的系统的数学。在这里，作者将这两个主题联系在一起，首先介绍 Levy 过程的一般理论，然后以直接且易于理解的方式开发 Levy 过程的随机微积分。这个经过全面修订的版本现在包含许多新主题。其中包括：正则变化和次指数分布； Levy 过程具有有限矩的充分必要条件；具有有限变化的 Levy 过程的表征； Kunita 对 Levy 型随机积分矩的估计；一般 Levy 过程的 Ito 表示和鞅表示定理的新证明；多重 Wiener-Levy 积分和混沌分解；马利亚文微积分简介； Levy 驱动的 SDE 的稳定性理论简介。
Levy processes form a wide and rich class of random process, and have many applications ranging from physics to finance. Stochastic calculus is the mathematics of systems interacting with random noise. Here, the author ties these two subjects together, beginning with an introduction to the general theory of Levy processes, then leading on to develop the stochastic calculus for Levy processes in a direct and accessible way. This fully revised edition now features a number of new topics. These include: regular variation and subexponential distributions; necessary and sufficient conditions for Levy processes to have finite moments; characterisation of Levy processes with finite variation; Kunita's estimates for moments of Levy type stochastic integrals; new proofs of Ito representation and martingale representation theorems for general Levy processes; multiple Wiener-Levy integrals and chaos decomposition; an introduction to Malliavin calculus; an introduction to stability theory for Levy-driven SDEs.