In applications, and especially in mathematical finance, random time-dependent events are often modeled as stochastic processes. Assumptions are made aboutthe structure of such processes, and serious researchers will want to justifythose assumptions through the use of data. As statisticians are wont to say,“In God we trust; all others must bring data.”. . This book establishes the theory of how to go about estimating not just scalar parameters about a proposed model, but also the underlying structure of the model itself. Classic statistical tools are used: the law of large numbers, and the central limit theorem. Researchers have recently developed creative and original methods to use these tools in sophisticated (but highly technical) ways to reveal new details about the underlying structure. For the first time in book form, the authors present these latest techniques, based on research from the last 10 years. They include new findings. . This book will be of special interest to researchers,combining the theory of mathematical finance with its investigation using market data, and it will also prove to be useful in a broad range of applications, such as to mathematical biology, chemical engineering, and physics. The first and so far the only book in this area. Presents the important results in a coherent and unified manner. Includes systematic, creative and original ways to use sophisticated (but highly technical) tools . INDICE: Part I Introduction and Preliminary Material. 1.Introduction. 2.Some Prerequisites. Part II The Basic Results. 3.Laws of Large Numbers: the Basic Results. 4.Central Limit Theorems: Technical Tools. 5.Central Limit Theorems: the Basic Results. 6.Integrated Discretization Error. Part III More Laws of Large Numbers. 7.First Extension: Random Weights. 8.Second Extension: Functions of Several Increments. 9.Third Extension: Truncated Functionals. Part IV Extensions of the Central Limit Theorems. 10.The Central Limit Theorem for RandomWeights. 11.The Central Limit Theorem for Functions of a Finite Number of Increments. 12.The Central Limit Theorem for Functions of an Increasing Number ofIncrements. 13.The Central Limit Theorem for Truncated Functionals. Part V Various Extensions. 14.Irregular Discretization Schemes. 15.Higher Order Limit Theorems. 16.Semimartingales Contaminated by Noise. Appendix. References. Assumptions. Index of Functionals. Index.
- ISBN: 978-3-642-24126-0
- Editorial: Springer Berlin Heidelberg
- Encuadernacion: Cartoné
- Páginas: 596
- Fecha Publicación: 23/10/2011
- Nº Volúmenes: 1
- Idioma: Inglés