Asymptotic Stochastics
| Author | : Norbert Henze |
| Publisher | : Springer Nature |
| Total Pages | : 470 |
| Release | : |
| Genre | : |
| ISBN | : 3662689235 |
Asymptotic Stochastics
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Asymptotic Methods in Stochastics
| Author | : M. Csörgö |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 546 |
| Release | : 2004 |
| Genre | : Mathematics |
| ISBN | : 0821835610 |
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 Analysis for Functional Stochastic Differential Equations
| Author | : Jianhai Bao |
| Publisher | : Springer |
| Total Pages | : 159 |
| Release | : 2016-11-19 |
| Genre | : Mathematics |
| ISBN | : 3319469797 |
This brief treats dynamical systems that involve delays and random disturbances. The study is motivated by a wide variety of systems in real life in which random noise has to be taken into consideration and the effect of delays cannot be ignored. Concentrating on such systems that are described by functional stochastic differential equations, this work focuses on the study of large time behavior, in particular, ergodicity.This brief is written for probabilists, applied mathematicians, engineers, and scientists who need to use delay systems and functional stochastic differential equations in their work. Selected topics from the brief can also be used in a graduate level topics course in probability and stochastic processes.
Asymptotic Laws and Methods in Stochastics
| Author | : Donald Dawson |
| Publisher | : Springer |
| Total Pages | : 401 |
| Release | : 2015-11-12 |
| Genre | : Mathematics |
| ISBN | : 1493930761 |
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
| Author | : Yuri Kabanov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 274 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 3662132427 |
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 and Analytic Methods in Stochastic Evolutionary Symptoms
| Author | : Dmitri Koroliouk |
| Publisher | : John Wiley & Sons |
| Total Pages | : 276 |
| Release | : 2023-08-29 |
| Genre | : Mathematics |
| ISBN | : 1786309114 |
This book illustrates a number of asymptotic and analytic approaches applied for the study of random evolutionary systems, and considers typical problems for specific examples. In this case, constructive mathematical models of natural processes are used, which more realistically describe the trajectories of diffusion-type processes, rather than those of the Wiener process. We examine models where particles have some free distance between two consecutive collisions. At the same time, we investigate two cases: the Markov evolutionary system, where the time during which the particle moves towards some direction is distributed exponentially with intensity parameter λ; and the semi-Markov evolutionary system, with arbitrary distribution of the switching process. Thus, the models investigated here describe the motion of particles with a finite speed and the proposed random evolutionary process with characteristics of a natural physical process: free run and finite propagation speed. In the proposed models, the number of possible directions of evolution can be finite or infinite.
Asymptotic Methods in the Theory of Stochastic Differential Equations
| Author | : A. V. Skorokhod |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 362 |
| Release | : 2009-01-07 |
| Genre | : Mathematics |
| ISBN | : 9780821898253 |
Ergodic theorems: General ergodic theorems Densities for transition probabilities and resolvents for Markov solutions of stochastic differential equations Ergodic theorems for one-dimensional stochastic equations Ergodic theorems for solutions of stochastic equations in $R^d$ Asymptotic behavior of systems of stochastic equations containing a small parameter: Equations with a small right-hand side Processes with rapid switching Averaging over variables for systems of stochastic differential equations Stability. Linear systems: Stability of sample paths of homogeneous Markov processes Linear equations in $R^d$ and the stochastic semigroups connected with them. Stability Stability of solutions of stochastic differential equations Linear stochastic equations in Hilbert space. Stochastic semigroups. Stability: Linear equations with bounded coefficients Strong stochastic semigroups with second moments Stability Bibliography
Asymptotic Analysis of Unstable Solutions of Stochastic Differential Equations
| Author | : Grigorij Kulinich |
| Publisher | : Springer Nature |
| Total Pages | : 240 |
| Release | : 2020-04-29 |
| Genre | : Mathematics |
| ISBN | : 3030412911 |
This book is devoted to unstable solutions of stochastic differential equations (SDEs). Despite the huge interest in the theory of SDEs, this book is the first to present a systematic study of the instability and asymptotic behavior of the corresponding unstable stochastic systems. The limit theorems contained in the book are not merely of purely mathematical value; rather, they also have practical value. Instability or violations of stability are noted in many phenomena, and the authors attempt to apply mathematical and stochastic methods to deal with them. The main goals include exploration of Brownian motion in environments with anomalies and study of the motion of the Brownian particle in layered media. A fairly wide class of continuous Markov processes is obtained in the limit. It includes Markov processes with discontinuous transition densities, processes that are not solutions of any Itô's SDEs, and the Bessel diffusion process. The book is self-contained, with presentation of definitions and auxiliary results in an Appendix. It will be of value for specialists in stochastic analysis and SDEs, as well as for researchers in other fields who deal with unstable systems and practitioners who apply stochastic models to describe phenomena of instability.
Asymptotic Methods and Stochastic Models in Problems of Wave Propagation
| Author | : Georgiĭ Ivanovich Petrashenʹ |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 264 |
| Release | : 1971 |
| Genre | : Mathematics |
| ISBN | : 9780821818954 |
Papers and articles about modeling and problems with wave propagation.
Large Deviations and Asymptotic Methods in Finance
| Author | : Peter K. Friz |
| Publisher | : Springer |
| Total Pages | : 590 |
| Release | : 2015-06-16 |
| Genre | : Mathematics |
| ISBN | : 3319116053 |
Topics covered in this volume (large deviations, differential geometry, asymptotic expansions, central limit theorems) give a full picture of the current advances in the application of asymptotic methods in mathematical finance, and thereby provide rigorous solutions to important mathematical and financial issues, such as implied volatility asymptotics, local volatility extrapolation, systemic risk and volatility estimation. This volume gathers together ground-breaking results in this field by some of its leading experts. Over the past decade, asymptotic methods have played an increasingly important role in the study of the behaviour of (financial) models. These methods provide a useful alternative to numerical methods in settings where the latter may lose accuracy (in extremes such as small and large strikes, and small maturities), and lead to a clearer understanding of the behaviour of models, and of the influence of parameters on this behaviour. Graduate students, researchers and practitioners will find this book very useful, and the diversity of topics will appeal to people from mathematical finance, probability theory and differential geometry.
