Fractional Stochastic Differential Equations

Author : Abdon Atangana,Seda İgret Araz
Publisher : Springer Nature
Page : 552 pages
File Size : 40,5 Mb
Release : 2022-04-22
Category : Mathematics
ISBN : 9789811907296

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Fractional Stochastic Differential Equations by Abdon Atangana,Seda İgret Araz Pdf

This book provides a thorough conversation on the underpinnings of Covid-19 spread modelling by using stochastics nonlocal differential and integral operators with singular and non-singular kernels. The book presents the dynamic of Covid-19 spread behaviour worldwide. It is noticed that the spread dynamic followed process with nonlocal behaviours which resemble power law, fading memory, crossover and stochastic behaviours. Fractional stochastic differential equations are therefore used to model spread behaviours in different parts of the worlds. The content coverage includes brief history of Covid-19 spread worldwide from December 2019 to September 2021, followed by statistical analysis of collected data for infected, death and recovery classes.

Author : Francesca Biagini,Yaozhong Hu,Bernt Øksendal,Tusheng Zhang
Publisher : Springer Science & Business Media
Page : 331 pages
File Size : 46,8 Mb
Release : 2008-02-17
Category : Mathematics
ISBN : 9781846287978

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Stochastic Calculus for Fractional Brownian Motion and Applications by Francesca Biagini,Yaozhong Hu,Bernt Øksendal,Tusheng Zhang Pdf

The purpose of this book is to present a comprehensive account of the different definitions of stochastic integration for fBm, and to give applications of the resulting theory. Particular emphasis is placed on studying the relations between the different approaches. Readers are assumed to be familiar with probability theory and stochastic analysis, although the mathematical techniques used in the book are thoroughly exposed and some of the necessary prerequisites, such as classical white noise theory and fractional calculus, are recalled in the appendices. This book will be a valuable reference for graduate students and researchers in mathematics, biology, meteorology, physics, engineering and finance.

Author : Evariste Giné,Christian Houdré,David Nualart
Publisher : Birkhäuser
Page : 362 pages
File Size : 55,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034880695

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Stochastic Inequalities and Applications by Evariste Giné,Christian Houdré,David Nualart Pdf

Concentration inequalities, which express the fact that certain complicated random variables are almost constant, have proven of utmost importance in many areas of probability and statistics. This volume contains refined versions of these inequalities, and their relationship to many applications particularly in stochastic analysis. The broad range and the high quality of the contributions make this book highly attractive for graduates, postgraduates and researchers in the above areas.

Author : Damien Lamberton,Bernard Lapeyre
Publisher : CRC Press
Page : 253 pages
File Size : 41,9 Mb
Release : 2011-12-14
Category : Business & Economics
ISBN : 9781420009941

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Introduction to Stochastic Calculus Applied to Finance by Damien Lamberton,Bernard Lapeyre Pdf

Since the publication of the first edition of this book, the area of mathematical finance has grown rapidly, with financial analysts using more sophisticated mathematical concepts, such as stochastic integration, to describe the behavior of markets and to derive computing methods. Maintaining the lucid style of its popular predecessor, this concise and accessible introduction covers the probabilistic techniques required to understand the most widely used financial models. Along with additional exercises, this edition presents fully updated material on stochastic volatility models and option pricing as well as a new chapter on credit risk modeling. It contains many numerical experiments and real-world examples taken from the authors' own experiences. The book also provides all of the necessary stochastic calculus theory and implements some of the algorithms using SciLab. Key topics covered include martingales, arbitrage, option pricing, and the Black-Scholes model.

Author : Mark M. Meerschaert,Alla Sikorskii
Publisher : Walter de Gruyter GmbH & Co KG
Page : 421 pages
File Size : 50,8 Mb
Release : 2019-10-21
Category : Mathematics
ISBN : 9783110559149

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Stochastic Models for Fractional Calculus by Mark M. Meerschaert,Alla Sikorskii Pdf

Fractional calculus is a rapidly growing field of research, at the interface between probability, differential equations, and mathematical physics. It is used to model anomalous diffusion, in which a cloud of particles spreads in a different manner than traditional diffusion. This monograph develops the basic theory of fractional calculus and anomalous diffusion, from the point of view of probability. In this book, we will see how fractional calculus and anomalous diffusion can be understood at a deep and intuitive level, using ideas from probability. It covers basic limit theorems for random variables and random vectors with heavy tails. This includes regular variation, triangular arrays, infinitely divisible laws, random walks, and stochastic process convergence in the Skorokhod topology. The basic ideas of fractional calculus and anomalous diffusion are closely connected with heavy tail limit theorems. Heavy tails are applied in finance, insurance, physics, geophysics, cell biology, ecology, medicine, and computer engineering. The goal of this book is to prepare graduate students in probability for research in the area of fractional calculus, anomalous diffusion, and heavy tails. Many interesting problems in this area remain open. This book will guide the motivated reader to understand the essential background needed to read and unerstand current research papers, and to gain the insights and techniques needed to begin making their own contributions to this rapidly growing field.

Author : Yuliya Mishura
Publisher : Springer
Page : 398 pages
File Size : 47,8 Mb
Release : 2008-04-12
Category : Mathematics
ISBN : 9783540758730

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Stochastic Calculus for Fractional Brownian Motion and Related Processes by Yuliya Mishura Pdf

This volume examines the theory of fractional Brownian motion and other long-memory processes. Interesting topics for PhD students and specialists in probability theory, stochastic analysis and financial mathematics demonstrate the modern level of this field. It proves that the market with stock guided by the mixed model is arbitrage-free without any restriction on the dependence of the components and deduces different forms of the Black-Scholes equation for fractional market.

Author : Sabir Umarov,Marjorie Hahn,Kei Kobayashi
Publisher : World Scientific
Page : 192 pages
File Size : 41,5 Mb
Release : 2018-02-13
Category : Mathematics
ISBN : 9789813230996

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Beyond The Triangle: Brownian Motion, Ito Calculus, And Fokker-planck Equation - Fractional Generalizations by Sabir Umarov,Marjorie Hahn,Kei Kobayashi Pdf

The book is devoted to the fundamental relationship between three objects: a stochastic process, stochastic differential equations driven by that process and their associated Fokker-Planck-Kolmogorov equations. This book discusses wide fractional generalizations of this fundamental triple relationship, where the driving process represents a time-changed stochastic process; the Fokker-Planck-Kolmogorov equation involves time-fractional order derivatives and spatial pseudo-differential operators; and the associated stochastic differential equation describes the stochastic behavior of the solution process. It contains recent results obtained in this direction.This book is important since the latest developments in the field, including the role of driving processes and their scaling limits, the forms of corresponding stochastic differential equations, and associated FPK equations, are systematically presented. Examples and important applications to various scientific, engineering, and economics problems make the book attractive for all interested researchers, educators, and graduate students.

Author : Sabir Umarov
Publisher : Springer
Page : 434 pages
File Size : 52,8 Mb
Release : 2015-08-18
Category : Mathematics
ISBN : 9783319207711

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Introduction to Fractional and Pseudo-Differential Equations with Singular Symbols by Sabir Umarov Pdf

The book systematically presents the theories of pseudo-differential operators with symbols singular in dual variables, fractional order derivatives, distributed and variable order fractional derivatives, random walk approximants, and applications of these theories to various initial and multi-point boundary value problems for pseudo-differential equations. Fractional Fokker-Planck-Kolmogorov equations associated with a large class of stochastic processes are presented. A complex version of the theory of pseudo-differential operators with meromorphic symbols based on the recently introduced complex Fourier transform is developed and applied for initial and boundary value problems for systems of complex differential and pseudo-differential equations.

Author : Simo Särkkä,Arno Solin
Publisher : Cambridge University Press
Page : 327 pages
File Size : 43,8 Mb
Release : 2019-05-02
Category : Business & Economics
ISBN : 9781316510087

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Applied Stochastic Differential Equations by Simo Särkkä,Arno Solin Pdf

With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.

Author : N El Karoui,Laurent Mazliak
Publisher : CRC Press
Page : 236 pages
File Size : 44,5 Mb
Release : 1997-01-17
Category : Mathematics
ISBN : 0582307333

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Backward Stochastic Differential Equations by N El Karoui,Laurent Mazliak Pdf

This book presents the texts of seminars presented during the years 1995 and 1996 at the Université Paris VI and is the first attempt to present a survey on this subject. Starting from the classical conditions for existence and unicity of a solution in the most simple case-which requires more than basic stochartic calculus-several refinements on the hypotheses are introduced to obtain more general results.

Author : Sabir Umarov,Marjorie G. Hahn,Kei Kobayashi (Mathematics professor)
Publisher : Unknown
Page : 192 pages
File Size : 47,5 Mb
Release : 2017
Category : MATHEMATICS
ISBN : 9813230924

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Beyond the Triangle by Sabir Umarov,Marjorie G. Hahn,Kei Kobayashi (Mathematics professor) Pdf

Author : Bernt Oksendal
Publisher : Springer Science & Business Media
Page : 218 pages
File Size : 43,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662130506

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Stochastic Differential Equations by Bernt Oksendal Pdf

These notes are based on a postgraduate course I gave on stochastic differential equations at Edinburgh University in the spring 1982. No previous knowledge about the subject was assumed, but the presen tation is based on some background in measure theory. There are several reasons why one should learn more about stochastic differential equations: They have a wide range of applica tions outside mathematics, there are many fruitful connections to other mathematical disciplines and the subject has a rapidly develop ing life of its own as a fascinating research field with many interesting unanswered questions. Unfortunately most of the literature about stochastic differential equations seems to place so much emphasis on rigor and complete ness that is scares many nonexperts away. These notes are an attempt to approach the subject from the nonexpert point of view: Not knowing anything (except rumours, maybe) about a subject to start with, what would I like to know first of all? My answer would be: 1) In what situations does the subject arise? 2) What are its essential features? 3) What are the applications and the connections to other fields? I would not be so interested in the proof of the most general case, but rather in an easier proof of a special case, which may give just as much of the basic idea in the argument. And I would be willing to believe some basic results without proof (at first stage, anyway) in order to have time for some more basic applications.

Author : Carlos A. Braumann
Publisher : John Wiley & Sons
Page : 304 pages
File Size : 52,9 Mb
Release : 2019-03-08
Category : Mathematics
ISBN : 9781119166078

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Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance by Carlos A. Braumann Pdf

A comprehensive introduction to the core issues of stochastic differential equations and their effective application Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance offers a comprehensive examination to the most important issues of stochastic differential equations and their applications. The author — a noted expert in the field — includes myriad illustrative examples in modelling dynamical phenomena subject to randomness, mainly in biology, bioeconomics and finance, that clearly demonstrate the usefulness of stochastic differential equations in these and many other areas of science and technology. The text also features real-life situations with experimental data, thus covering topics such as Monte Carlo simulation and statistical issues of estimation, model choice and prediction. The book includes the basic theory of option pricing and its effective application using real-life. The important issue of which stochastic calculus, Itô or Stratonovich, should be used in applications is dealt with and the associated controversy resolved. Written to be accessible for both mathematically advanced readers and those with a basic understanding, the text offers a wealth of exercises and examples of application. This important volume: Contains a complete introduction to the basic issues of stochastic differential equations and their effective application Includes many examples in modelling, mainly from the biology and finance fields Shows how to: Translate the physical dynamical phenomenon to mathematical models and back, apply with real data, use the models to study different scenarios and understand the effect of human interventions Conveys the intuition behind the theoretical concepts Presents exercises that are designed to enhance understanding Offers a supporting website that features solutions to exercises and R code for algorithm implementation Written for use by graduate students, from the areas of application or from mathematics and statistics, as well as academics and professionals wishing to study or to apply these models, Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance is the authoritative guide to understanding the issues of stochastic differential equations and their application.

Author : Jaya P. N. Bishwal
Publisher : Springer
Page : 268 pages
File Size : 45,8 Mb
Release : 2007-09-26
Category : Mathematics
ISBN : 9783540744481

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Parameter Estimation in Stochastic Differential Equations by Jaya P. N. Bishwal Pdf

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 : Peter H. Baxendale,Sergey V. Lototsky
Publisher : World Scientific
Page : 416 pages
File Size : 43,6 Mb
Release : 2007
Category : Science
ISBN : 9789812706621

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Stochastic Differential Equations by Peter H. Baxendale,Sergey V. Lototsky Pdf

The first paper in the volume, Stochastic Evolution Equations by N V Krylov and B L Rozovskii, was originally published in Russian in 1979. After more than a quarter-century, this paper remains a standard reference in the field of stochastic partial differential equations (SPDEs) and continues to attract attention of mathematicians of all generations, because, together with a short but thorough introduction to SPDEs, it presents a number of optimal and essentially non-improvable results about solvability for a large class of both linear and non-linear equations.