Asymptotic Stochastics

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Asymptotic Stochastics

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Author : Norbert Henze
language : en
Publisher: Springer Nature
Release Date : 2024-10-19

Asymptotic Stochastics written by Norbert Henze and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-19 with Mathematics categories.

This textbook, which is based on the second edition of a book that has been previously published in German language, provides a comprehension-oriented introduction to asymptotic stochastics. It is aimed at the beginning of a master's degree course in mathematics and covers the material that can be taught in a four-hour lecture with two-hour exercises. Individual chapters are also suitable for seminars at the end of a bachelor's degree course. In addition to more basic topics such as the method of moments in connection with the convergence in distribution or the multivariate central limit theorem and the delta method, the book covers limit theorems for U-statistics, the Wiener process and Donsker's theorem, as well as the Brownian bridge, with applications to statistics. It concludes with a central limit theorem for triangular arrays of Hilbert space-valued random elements with applications to weighted L2 statistics. The book is deliberately designed forself-study. It contains 138 self-questions, which are answered at the end of each chapter, as well as 194 exercises with solutions. This book is a translation of an original German edition. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation.

Asymptotic Methods In Stochastics

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Author : M. Csörgö
language : en
Publisher: American Mathematical Soc.
Release Date : 2004

Asymptotic Methods In Stochastics written by M. Csörgö and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.

Honoring over forty years of Miklos Csorgo's work in probability and statistics, this title shows the state of the research. This book covers such topics as: path properties of stochastic processes, weak convergence of random size sums, almost sure stability of weighted maxima, and procedures for detecting changes in statistical models.

Asymptotic Laws And Methods In Stochastics

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Author : Donald Dawson
language : en
Publisher: Springer
Release Date : 2015-11-12

Asymptotic Laws And Methods In Stochastics written by Donald Dawson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-12 with Mathematics categories.

This book contains articles arising from a conference in honour of mathematician-statistician Miklόs Csörgő on the occasion of his 80th birthday, held in Ottawa in July 2012. It comprises research papers and overview articles, which provide a substantial glimpse of the history and state-of-the-art of the field of asymptotic methods in probability and statistics, written by leading experts. The volume consists of twenty articles on topics on limit theorems for self-normalized processes, planar processes, the central limit theorem and laws of large numbers, change-point problems, short and long range dependent time series, applied probability and stochastic processes, and the theory and methods of statistics. It also includes Csörgő’s list of publications during more than 50 years, since 1962.

Two Scale Stochastic Systems

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Author : Yuri Kabanov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Two Scale Stochastic Systems written by Yuri Kabanov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.

Two-scale systems described by singularly perturbed SDEs have been the subject of ample literature. However, this new monograph develops subjects that were rarely addressed and could be given the collective description "Stochastic Tikhonov-Levinson theory and its applications." The book provides a mathematical apparatus designed to analyze the dynamic behaviour of a randomly perturbed system with fast and slow variables. In contrast to the deterministic Tikhonov-Levinson theory, the basic model is described in a more realistic way by stochastic differential equations. This leads to a number of new theoretical questions but simultaneously allows us to treat in a unified way a surprisingly wide spectrum of applications like fast modulations, approximate filtering, and stochastic approximation.Two-scale systems described by singularly perturbed SDEs have been the subject of ample literature. However, this new monograph develops subjects that were rarely addressed and could be given the collective description "Stochastic Tikhonov-Levinson theory and its applications." The book provides a mathematical apparatus designed to analyze the dynamic behaviour of a randomly perturbed system with fast and slow variables. In contrast to the deterministic Tikhonov-Levinson theory, the basic model is described in a more realistic way by stochastic differential equations. This leads to a number of new theoretical questions but simultaneously allows us to treat in a unified way a surprisingly wide spectrum of applications like fast modulations, approximate filtering, and stochastic approximation.

Asymptotic Analyses For Complex Evolutionary Systems With Markov And Semi Markov Switching Using Approximation Schemes

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Author : Yaroslav Chabanyuk
language : en
Publisher: John Wiley & Sons
Release Date : 2020-10-02

Asymptotic Analyses For Complex Evolutionary Systems With Markov And Semi Markov Switching Using Approximation Schemes written by Yaroslav Chabanyuk and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-02 with Mathematics categories.

This book analyzes stochastic evolutionary models under the impulse of diffusion, as well as Markov and semi-Markov switches. Models are investigated under the conditions of classical and non-classical (Levy and Poisson) approximations in addition to jumping stochastic approximations and continuous optimization procedures. Among other asymptotic properties, particular attention is given to weak convergence, dissipativity, stability and the control of processes and their generators. Weak convergence of stochastic processes is usually proved by verifying two conditions: the tightness of the distributions of the converging processes, which ensures the existence of a converging subsequence, and the uniqueness of the weak limit. Achieving the limit can be done on the semigroups that correspond to the converging process as well as on appropriate generators. While this provides the convergence of generators, a natural question arises concerning the uniqueness of a limit semigroup.

Stochastics In Finite And Infinite Dimensions

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Author : Takeyuki Hida
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Stochastics In Finite And Infinite Dimensions written by Takeyuki Hida and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

During the last fifty years, Gopinath Kallianpur has made extensive and significant contributions to diverse areas of probability and statistics, including stochastic finance, Fisher consistent estimation, non-linear prediction and filtering problems, zero-one laws for Gaussian processes and reproducing kernel Hilbert space theory, and stochastic differential equations in infinite dimensions. To honor Kallianpur's pioneering work and scholarly achievements, a number of leading experts have written research articles highlighting progress and new directions of research in these and related areas. This commemorative volume, dedicated to Kallianpur on the occasion of his seventy-fifth birthday, will pay tribute to his multi-faceted achievements and to the deep insight and inspiration he has so graciously offered his students and colleagues throughout his career. Contributors to the volume: S. Aida, N. Asai, K. B. Athreya, R. N. Bhattacharya, A. Budhiraja, P. S. Chakraborty, P. Del Moral, R. Elliott, L. Gawarecki, D. Goswami, Y. Hu, J. Jacod, G. W. Johnson, L. Johnson, T. Koski, N. V. Krylov, I. Kubo, H.-H. Kuo, T. G. Kurtz, H. J. Kushner, V. Mandrekar, B. Margolius, R. Mikulevicius, I. Mitoma, H. Nagai, Y. Ogura, K. R. Parthasarathy, V. Perez-Abreu, E. Platen, B. V. Rao, B. Rozovskii, I. Shigekawa, K. B. Sinha, P. Sundar, M. Tomisaki, M. Tsuchiya, C. Tudor, W. A. Woycynski, J. Xiong.

Contributions To Stochastics

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Author : Sendler
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Contributions To Stochastics written by Sendler and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Since the contributions to this volume stem from very different fields, no attempt was made to find a systematic ordering. All results are new in so far as they have not been published so far.

Stochastic Analysis Stochastic Systems And Applications To Finance

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Author : Allanus Hak-Man Tsoi
language : en
Publisher: World Scientific
Release Date : 2011

Stochastic Analysis Stochastic Systems And Applications To Finance written by Allanus Hak-Man Tsoi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Business & Economics categories.

Pt. I. Stochastic analysis and systems. 1. Multidimensional Wick-Ito formula for Gaussian processes / D. Nualart and S. Ortiz-Latorre. 2. Fractional white noise multiplication / A.H. Tsoi. 3. Invariance principle of regime-switching diffusions / C. Zhu and G. Yin -- pt. II. Finance and stochastics. 4. Real options and competition / A. Bensoussan, J.D. Diltz and S.R. Hoe. 5. Finding expectations of monotone functions of binary random variables by simulation, with applications to reliability, finance, and round robin tournaments / M. Brown, E.A. Pekoz and S.M. Ross. 6. Filtering with counting process observations and other factors : applications to bond price tick data / X. Hu, D.R. Kuipers and Y. Zeng. 7. Jump bond markets some steps towards general models in applications to hedging and utility problems / M. Kohlmann and D. Xiong. 8. Recombining tree for regime-switching model : algorithm and weak convergence / R.H. Liu. 9. Optimal reinsurance under a jump diffusion model / S. Luo. 10. Applications of counting processes and martingales in survival analysis / J. Sun. 11. Stochastic algorithms and numerics for mean-reverting asset trading / Q. Zhang, C. Zhuang and G. Yin

Issues In Statistics Decision Making And Stochastics 2013 Edition

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Author :
language : en
Publisher: ScholarlyEditions
Release Date : 2013-05-01

Issues In Statistics Decision Making And Stochastics 2013 Edition written by and has been published by ScholarlyEditions this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-01 with Mathematics categories.

Issues in Statistics, Decision Making, and Stochastics: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Regular and Chaotic Dynamics. The editors have built Issues in Statistics, Decision Making, and Stochastics: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Regular and Chaotic Dynamics in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Statistics, Decision Making, and Stochastics: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Multiscale Stochastic Volatility For Equity Interest Rate And Credit Derivatives

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Author : Jean-Pierre Fouque
language : en
Publisher: Cambridge University Press
Release Date : 2011-09-29

Multiscale Stochastic Volatility For Equity Interest Rate And Credit Derivatives written by Jean-Pierre Fouque and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-29 with Mathematics categories.

Building upon the ideas introduced in their previous book, Derivatives in Financial Markets with Stochastic Volatility, the authors study the pricing and hedging of financial derivatives under stochastic volatility in equity, interest-rate, and credit markets. They present and analyze multiscale stochastic volatility models and asymptotic approximations. These can be used in equity markets, for instance, to link the prices of path-dependent exotic instruments to market implied volatilities. The methods are also used for interest rate and credit derivatives. Other applications considered include variance-reduction techniques, portfolio optimization, forward-looking estimation of CAPM 'beta', and the Heston model and generalizations of it. 'Off-the-shelf' formulas and calibration tools are provided to ease the transition for practitioners who adopt this new method. The attention to detail and explicit presentation make this also an excellent text for a graduate course in financial and applied mathematics.