2nd Edition
By (author): Odile Pons
The book is aimed at graduate students and researchers with basic knowledge of Probability and Integration Theory. It introduces classical inequalities in vector and functional spaces with applications to probability. It also develops new extensions of the analytical inequalities, with sharper bounds and generalizations to the sum or the supremum of random variables, to martingales and to transformed Brownian motions. The proofs of many new results are presented in great detail. Original tools are developed for spatial point processes and stochastic integration with respect to local martingales in the plane.
This second edition covers properties of random variables and time continuous local martingales with a discontinuous predictable compensator, with exponential inequalities and new inequalities for their maximum variable and their p-variations. A chapter on stochastic calculus presents the exponential sub-martingales developed for stationary processes and their properties. Another chapter devoted itself to the renewal theory of processes and to semi-Markovian processes, branching processes and shock processes. The Chapman–Kolmogorov equations for strong semi-Markovian processes provide equations for their hitting times in a functional setting which extends the exponential properties of the Markovian processes.
Contents:
• Preliminaries
• Inequalities for Means and Integrals
• Analytic Inequalities
• Inequalities for Martingales
• Stochastic Calculus
• Functional Inequalities
• Markov Processes
• Inequalities for Processes
• Inequalities in Complex Spaces
• Appendix A: Probability
本帖隐藏的内容
原版 PDF:PDF 压缩包:
- Inequalities in Analysis and Probability (2nd Edition).pdf
如果你喜欢我分享的书籍,请关注我:
https://bbs.pinggu.org/z_guanzhu.php?action=add&fuid=5975757
订阅我的文库:
【金融 + 经济 + 商学 + 国际政治】
https://bbs.pinggu.org/forum.php?mod=collection&action=view&ctid=3257
【数学 + 统计 + 计算机编程】
https://bbs.pinggu.org/forum.php?mod=collection&action=view&ctid=3258
【历史 + 心理学 + 社会自然科学】
https://bbs.pinggu.org/forum.php?mod=collection&action=view&ctid=3259