Titlebook: Discretization of Processes; Jean Jacod,Philip Protter Book 2012 Springer-Verlag Berlin Heidelberg 2012 60F05, 60G44, 60H10, 60H35, 60J75,

Spina-Bifida

名字的误用

整洁

Some Prerequisitesf these topics are prerequisites for the rest of the book..In Sect. 2.1 the main properties of semimartingales are recalled, with a special emphasis on a description of the so-called .. We also recall basic features of the characteristics of a semimartingale. Most of the results established in this

Glaci冰

断言

Central Limit Theorems: Technical Tools chapter..The reason for presenting this material in a separate chapter is that Central Limit Theorems have rather long proofs, but for the functionals previously considered, as well as for more general functionals to be seen in the forthcoming chapters, the proofs are always based on the same ideas

Affable

易发怒

Integrated Discretization Errorbtained by discretization of the Itô semimartingale . along a regular grid with stepsize .., we study the integrated error: this can be . or, in the .. sense, ...In both cases, and if . is .., these functionals, suitably normalized, converge to a non-trivial limiting process. In the first case, the

使成核

First Extension: Random Weightsced by . for a function . on .×ℝ.×ℝ., where . is the dimension of ., and likewise for the functional .′.(.,.). The results are perhaps obvious generalizations of those of Chap. ., the main difficulty being to establish the assumptions on . ensuring the convergence..The motivation for this is to solv

阶层

Second Extension: Functions of Several Incrementsderlying process .. This covers two different situations: . In Sects. 8.2 and 8.3 the Laws of Large Numbers for the unnormalized functionals are presented, for a fixed number . or an increasing number .. of increments, respectively: the methods and results are deeply different in the two cases. In c

平淡而无味

Third Extension: Truncated Functionalsler (upward truncation) or bigger (downward truncation) in absolute value than some level ..>0. This level .. depends on the mesh .. and typically goes to 0 as ..→0. This allows one to disentangle the “jump part” and the “Brownian part” of the Itô semimartingale: when interested by jumps, one consid