Filtering And Parameter Estimation For Partially Observed Generalized Hawkes Processes PDF Download
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Author | : Anca Patricia Vacarescu |
Publisher | : Stanford University |
Total Pages | : 192 |
Release | : 2011 |
Genre | : |
ISBN | : |
Download Filtering and Parameter Estimation for Partially Observed Generalized Hawkes Processes Book in PDF, ePub and Kindle
We consider the nonlinear filtering problem for partially observed Generalized Hawkes Processes, which can be applied in the context of portfolio credit risk. The problem belongs to the larger class of hidden Markov models, where the counting process is observed at discrete points in time and the observations are sparse, while the intensity driving process in unobservable. We construct the conditional distribution of the process given the information filtration and we discuss the analytical and numerical properties of the corresponding filters. In particular, we study the sensitivity of the filters with respect to the parameters of the model, and we obtain a monotonicity result with respect to the jump and the volatility terms driving the intensity. Using the scaled process, we provide necessary and sufficient conditions for the frequency of time observations in terms of the parameters of the model, to ensure a good performance of the filter. We also address the problem of parameter estimation for the Generalized Hawkes Process in the framework of the EM algorithm, and we analyze the effect of the self-exciting feature of our process on the asymptotic and numerical properties of the estimators.
Author | : Anca Patricia Vacarescu |
Publisher | : |
Total Pages | : |
Release | : 2011 |
Genre | : |
ISBN | : |
Download Filtering and Parameter Estimation for Partially Observed Generalized Hawkes Processes Book in PDF, ePub and Kindle
We consider the nonlinear filtering problem for partially observed Generalized Hawkes Processes, which can be applied in the context of portfolio credit risk. The problem belongs to the larger class of hidden Markov models, where the counting process is observed at discrete points in time and the observations are sparse, while the intensity driving process in unobservable. We construct the conditional distribution of the process given the information filtration and we discuss the analytical and numerical properties of the corresponding filters. In particular, we study the sensitivity of the filters with respect to the parameters of the model, and we obtain a monotonicity result with respect to the jump and the volatility terms driving the intensity. Using the scaled process, we provide necessary and sufficient conditions for the frequency of time observations in terms of the parameters of the model, to ensure a good performance of the filter. We also address the problem of parameter estimation for the Generalized Hawkes Process in the framework of the EM algorithm, and we analyze the effect of the self-exciting feature of our process on the asymptotic and numerical properties of the estimators.
Author | : Tomasz R. Bielecki |
Publisher | : Cambridge University Press |
Total Pages | : 280 |
Release | : 2020-08-27 |
Genre | : Mathematics |
ISBN | : 1108895379 |
Download Structured Dependence between Stochastic Processes Book in PDF, ePub and Kindle
The relatively young theory of structured dependence between stochastic processes has many real-life applications in areas including finance, insurance, seismology, neuroscience, and genetics. With this monograph, the first to be devoted to the modeling of structured dependence between random processes, the authors not only meet the demand for a solid theoretical account but also develop a stochastic processes counterpart of the classical copula theory that exists for finite-dimensional random variables. Presenting both the technical aspects and the applications of the theory, this is a valuable reference for researchers and practitioners in the field, as well as for graduate students in pure and applied mathematics programs. Numerous theoretical examples are included, alongside examples of both current and potential applications, aimed at helping those who need to model structured dependence between dynamic random phenomena.
Author | : V.N. Fomin |
Publisher | : Springer Science & Business Media |
Total Pages | : 387 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9401153264 |
Download Optimal Filtering Book in PDF, ePub and Kindle
This book is devoted to an investigation of some important problems of mod ern filtering theory concerned with systems of 'any nature being able to per ceive, store and process an information and apply it for control and regulation'. (The above quotation is taken from the preface to [27]). Despite the fact that filtering theory is l'argely worked out (and its major issues such as the Wiener-Kolmogorov theory of optimal filtering of stationary processes and Kalman-Bucy recursive filtering theory have become classical) a development of the theory is far from complete. A great deal of recent activity in this area is observed, researchers are trying consistently to generalize famous results, extend them to more broad classes of processes, realize and justify more simple procedures for processing measurement data in order to obtain more efficient filtering algorithms. As to nonlinear filter ing, it remains much as fragmentary. Here much progress has been made by R. L. Stratonovich and his successors in the area of filtering of Markov processes. In this volume an effort is made to advance in certain of these issues. The monograph has evolved over many years, coming of age by stages. First it was an impressive job of gathering together the bulk of the impor tant contributions to estimation theory, an understanding and moderniza tion of some of its results and methods, with the intention of applying them to recursive filtering problems.
Author | : G. Kallianpur |
Publisher | : |
Total Pages | : 35 |
Release | : 1989 |
Genre | : |
ISBN | : |
Download Parameter Estimation in Linear Filtering Book in PDF, ePub and Kindle
Suppose on a probability space (omega, F, P) a partially observable random process (x sub l, Y sub 1, t> or = 0; is given where only the second component (y sub 1) is observed. Furthermore assume that (x sub 1, y sub 1) satisfy a certain system of stochastic differential equations driven by independent Wiener processes (W sub 1 (t)) and (W 2 (sub 2)). We obtain a large deviation inequality for the maximum likelihood estimator (m.l.e.) of the unknown parameter theta = (alpha, beta). This inequality enables us to prove the strong consistency, asymptotic normality and covergence of the moments of the m.l.e. The method of proof can be extended to obtain similar results when multi-dimensional instead of one dimensional processes are considered and theta is a k-dimensional vector. (KR).
Author | : 彭瑋翔 |
Publisher | : |
Total Pages | : |
Release | : 2013 |
Genre | : |
ISBN | : |
Download Parameter Estimation for Partially Observed ODE and Its Applications Book in PDF, ePub and Kindle
Author | : Patrick J. Laub |
Publisher | : Springer Nature |
Total Pages | : 134 |
Release | : 2022-01-03 |
Genre | : Mathematics |
ISBN | : 3030846393 |
Download The Elements of Hawkes Processes Book in PDF, ePub and Kindle
Hawkes processes are studied and used in a wide range of disciplines: mathematics, social sciences, and earthquake modelling, to name a few. This book presents a selective coverage of the core and recent topics in the broad field of Hawkes processes. It consists of three parts. Parts I and II summarise and provide an overview of core theory (including key simulation methods) and inference methods, complemented by a selection of recent research developments and applications. Part III is devoted to case studies in seismology and finance that connect the core theory and inference methods to practical scenarios. This book is designed primarily for applied probabilists, statisticians, and machine learners. However, the mathematical prerequisites have been kept to a minimum so that the content will also be of interest to undergraduates in advanced mathematics and statistics, as well as machine learning practitioners. Knowledge of matrix theory with basics of probability theory, including Poisson processes, is considered a prerequisite. Colour-blind-friendly illustrations are included.
Author | : |
Publisher | : |
Total Pages | : 812 |
Release | : 1997 |
Genre | : Mathematical statistics |
ISBN | : |
Download Current Index to Statistics, Applications, Methods and Theory Book in PDF, ePub and Kindle
The Current Index to Statistics (CIS) is a bibliographic index of publications in statistics, probability, and related fields.
Author | : |
Publisher | : |
Total Pages | : 378 |
Release | : 2008 |
Genre | : Dissertations, Academic |
ISBN | : |
Download Index to Theses with Abstracts Accepted for Higher Degrees by the Universities of Great Britain and Ireland and the Council for National Academic Awards Book in PDF, ePub and Kindle
Author | : Davar Khoshnevisan |
Publisher | : Springer Science & Business Media |
Total Pages | : 590 |
Release | : 2006-04-10 |
Genre | : Mathematics |
ISBN | : 0387216316 |
Download Multiparameter Processes Book in PDF, ePub and Kindle
Self-contained presentation: from elementary material to state-of-the-art research; Much of the theory in book-form for the first time; Connections are made between probability and other areas of mathematics, engineering and mathematical physics