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Author: Jaya P. N. Bishwal Publisher: Springer ISBN: 3540744487 Category : Mathematics Languages : en Pages : 271
Book Description
Parameter estimation in stochastic differential equations and stochastic partial differential equations is the science, art and technology of modeling complex phenomena. The subject has attracted researchers from several areas of mathematics. This volume presents the estimation of the unknown parameters in the corresponding continuous models based on continuous and discrete observations and examines extensively maximum likelihood, minimum contrast and Bayesian methods.
Author: Jaya P. N. Bishwal Publisher: Springer ISBN: 3540744487 Category : Mathematics Languages : en Pages : 271
Book Description
Parameter estimation in stochastic differential equations and stochastic partial differential equations is the science, art and technology of modeling complex phenomena. The subject has attracted researchers from several areas of mathematics. This volume presents the estimation of the unknown parameters in the corresponding continuous models based on continuous and discrete observations and examines extensively maximum likelihood, minimum contrast and Bayesian methods.
Author: Jaya P. N. Bishwal Publisher: Springer Nature ISBN: 3031038614 Category : Mathematics Languages : en Pages : 634
Book Description
This book develops alternative methods to estimate the unknown parameters in stochastic volatility models, offering a new approach to test model accuracy. While there is ample research to document stochastic differential equation models driven by Brownian motion based on discrete observations of the underlying diffusion process, these traditional methods often fail to estimate the unknown parameters in the unobserved volatility processes. This text studies the second order rate of weak convergence to normality to obtain refined inference results like confidence interval, as well as nontraditional continuous time stochastic volatility models driven by fractional Levy processes. By incorporating jumps and long memory into the volatility process, these new methods will help better predict option pricing and stock market crash risk. Some simulation algorithms for numerical experiments are provided.
Author: Drumi D Bainov Publisher: World Scientific ISBN: 9814501883 Category : Mathematics Languages : en Pages : 246
Book Description
The question of the presence of various asymptotic properties of the solutions of ordinary differential equations arises when solving various practical problems. The investigation of these questions is still more important for impulsive differential equations which have a wider field of application than the ordinary ones.The results obtained by treating the asymptotic properties of the solutions of impulsive differential equations can be found in numerous separate articles. The systematized exposition of these results in a separate book will satisfy the growing interest in the problems related to the asymptotic properties of the solutions of impulsive differential equations and their applications.
Author: Dimit?r Ba?nov Publisher: World Scientific ISBN: 9810218230 Category : Mathematics Languages : en Pages : 246
Book Description
The question of the presence of various asymptotic properties of the solutions of ordinary differential equations arises when solving various practical problems. The investigation of these questions is still more important for impulsive differential equations which have a wider field of application than the ordinary ones.The results obtained by treating the asymptotic properties of the solutions of impulsive differential equations can be found in numerous separate articles. The systematized exposition of these results in a separate book will satisfy the growing interest in the problems related to the asymptotic properties of the solutions of impulsive differential equations and their applications.
Author: I.A. Ibragimov Publisher: Springer Science & Business Media ISBN: 1461262755 Category : Mathematics Languages : en Pages : 285
Book Description
The book deals mainly with three problems involving Gaussian stationary processes. The first problem consists of clarifying the conditions for mutual absolute continuity (equivalence) of probability distributions of a "random process segment" and of finding effective formulas for densities of the equiva lent distributions. Our second problem is to describe the classes of spectral measures corresponding in some sense to regular stationary processes (in par ticular, satisfying the well-known "strong mixing condition") as well as to describe the subclasses associated with "mixing rate". The third problem involves estimation of an unknown mean value of a random process, this random process being stationary except for its mean, i. e. , it is the problem of "distinguishing a signal from stationary noise". Furthermore, we give here auxiliary information (on distributions in Hilbert spaces, properties of sam ple functions, theorems on functions of a complex variable, etc. ). Since 1958 many mathematicians have studied the problem of equivalence of various infinite-dimensional Gaussian distributions (detailed and sys tematic presentation of the basic results can be found, for instance, in [23]). In this book we have considered Gaussian stationary processes and arrived, we believe, at rather definite solutions. The second problem mentioned above is closely related with problems involving ergodic theory of Gaussian dynamic systems as well as prediction theory of stationary processes.
Author: Yasuko Chikuse Publisher: Springer Science & Business Media ISBN: 0387215409 Category : Mathematics Languages : en Pages : 425
Book Description
Covering statistical analysis on the two special manifolds, the Stiefel manifold and the Grassmann manifold, this book is designed as a reference for both theoretical and applied statisticians. It will also be used as a textbook for a graduate course in multivariate analysis. It is assumed that the reader is familiar with the usual theory of univariate statistics and a thorough background in mathematics, in particular, knowledge of multivariate calculation techniques.
Author: Volodymyr Korolyuk Publisher: Springer Science & Business Media ISBN: 3319035126 Category : Mathematics Languages : en Pages : 352
Book Description
This volume presents an extensive overview of all major modern trends in applications of probability and stochastic analysis. It will be a great source of inspiration for designing new algorithms, modeling procedures and experiments. Accessible to researchers, practitioners, as well as graduate and postgraduate students, this volume presents a variety of new tools, ideas and methodologies in the fields of optimization, physics, finance, probability, hydrodynamics, reliability, decision making, mathematical finance, mathematical physics and economics. Contributions to this Work include those of selected speakers from the international conference entitled “Modern Stochastics: Theory and Applications III,” held on September 10 –14, 2012 at Taras Shevchenko National University of Kyiv, Ukraine. The conference covered the following areas of research in probability theory and its applications: stochastic analysis, stochastic processes and fields, random matrices, optimization methods in probability, stochastic models of evolution systems, financial mathematics, risk processes and actuarial mathematics and information security.
Author: Yury A. Kutoyants Publisher: Springer Science & Business Media ISBN: 144713866X Category : Mathematics Languages : en Pages : 493
Book Description
The first book in inference for stochastic processes from a statistical, rather than a probabilistic, perspective. It provides a systematic exposition of theoretical results from over ten years of mathematical literature and presents, for the first time in book form, many new techniques and approaches.
Author: M. Sh Birman Publisher: American Mathematical Soc. ISBN: 9780821841068 Category : Differential equations Languages : en Pages : 218
Book Description
The Leningrad Seminar on mathematical physics, begun in 1947 by V. I. Smirnov and now run by O. A. Ladyzhenskaya, is sponsored by Leningrad University and the Leningrad Branch of the Steklov Mathematical Institute of the Academy of Sciences of the USSR. The main topics of the seminar center on the theory of boundary value problems and related questions of analysis and mathematical physics. This volume contains adaptations of lectures presented at the seminar during the academic year 1989-1990. For the most part, the papers are devoted to investigations of the spectrum of the Schrödinger operator (or its generalizations) perturbed by some relatively compact operator. The book studies the discrete spectrum that emerges in the spectral gaps of the nonperturbed operator, and considers the corresponding estimates and asymptotic formulas for spectrum distribution functions in the large-coupling-constant limit. The starting point here is the opening paper, which is devoted to the important case of a semi-infinite gap. The book also covers the case of inner gaps, related questions in the theory of functions, and an integral equation with difference kernel on a finite interval. The collection concludes with a paper focusing on the classical problem of constructing scattering theory for the Schrödinger operator with potential decreasing faster than the Coulomb potential
Author: Jaya P. N. Bishwal
Author: Jaya P. N. Bishwal
Author: Jaya P. N. Bishwal
Author: Drumi D Bainov
Author: Dimit?r Ba?nov
Author: I.A. Ibragimov
Author: Yasuko Chikuse
Author: 
Author: Volodymyr Korolyuk
Author: Yury A. Kutoyants
Author: M. Sh Birman