Statistical Inference for Fractional Diffusion Processes
Statistical Inference for Fractional Diffusion Processes

Author: B. L. S. Prakasa Rao

Publisher: John Wiley & Sons

Published: 2011-07-05

Total Pages: 213

ISBN-13: 0470975768

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Stochastic processes are widely used for model building in the social, physical, engineering and life sciences as well as in financial economics. In model building, statistical inference for stochastic processes is of great importance from both a theoretical and an applications point of view. This book deals with Fractional Diffusion Processes and statistical inference for such stochastic processes. The main focus of the book is to consider parametric and nonparametric inference problems for fractional diffusion processes when a complete path of the process over a finite interval is observable. Key features: Introduces self-similar processes, fractional Brownian motion and stochastic integration with respect to fractional Brownian motion. Provides a comprehensive review of statistical inference for processes driven by fractional Brownian motion for modelling long range dependence. Presents a study of parametric and nonparametric inference problems for the fractional diffusion process. Discusses the fractional Brownian sheet and infinite dimensional fractional Brownian motion. Includes recent results and developments in the area of statistical inference of fractional diffusion processes. Researchers and students working on the statistics of fractional diffusion processes and applied mathematicians and statisticians involved in stochastic process modelling will benefit from this book.

Select Topics of Econophysics
Select Topics of Econophysics

Author: Amit Sinha

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2024-11-04

Total Pages: 484

ISBN-13: 3110987589

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Economics requires understanding and analyzing forces that bring buyers and sellers to a market place who then negotiate exchanges of goods and services based on a mutually agreeable price. Economists have their own method of modeling whereby models are first conceived of some notion of economic and financial thinking, before being empirically tested, and anomalies are then recognized if the observed data is inconsistent with the hypothetical underpinning. This is in inherent contradiction with the modeling approaches of physicists who develop their theories, principle and laws after observing empirical data. The awareness that physics can enlighten the understanding of human behavior (and thus economics), and the interest of physicists in applying their training and models to understanding the complexities of finance and economics, led to the creation of a new field of study appropriately termed as Econophysics. Selected Topics on Econophysics is a collection of essays on topics that enhance and enrich our understanding of economic modeling when the same rigor of modelling used by physicists is brought to developing financial and economic theories. These articles include discussions on modeling bitcoins, stock index modeling using geometric Brownian motion, agent-based modeling, wealth distribution modeling, as well as modeling related to fractal regression, and chaotic processes. This interdisciplinary book will interest researchers, graduate students and professionals in the fields of economics, finance as well as physics.

Nonlinear Mathematics for Uncertainty and its Applications
Nonlinear Mathematics for Uncertainty and its Applications

Author: Shoumei Li

Publisher: Springer Science & Business Media

Published: 2011-07-21

Total Pages: 708

ISBN-13: 364222833X

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This volume is a collection of papers presented at the international conference on Nonlinear Mathematics for Uncertainty and Its Applications (NLMUA2011), held at Beijing University of Technology during the week of September 7--9, 2011. The conference brought together leading researchers and practitioners involved with all aspects of nonlinear mathematics for uncertainty and its applications. Over the last fifty years there have been many attempts in extending the theory of classical probability and statistical models to the generalized one which can cope with problems of inference and decision making when the model-related information is scarce, vague, ambiguous, or incomplete. Such attempts include the study of nonadditive measures and their integrals, imprecise probabilities and random sets, and their applications in information sciences, economics, finance, insurance, engineering, and social sciences. The book presents topics including nonadditive measures and nonlinear integrals, Choquet, Sugeno and other types of integrals, possibility theory, Dempster-Shafer theory, random sets, fuzzy random sets and related statistics, set-valued and fuzzy stochastic processes, imprecise probability theory and related statistical models, fuzzy mathematics, nonlinear functional analysis, information theory, mathematical finance and risk managements, decision making under various types of uncertainty, and others.

Mathematical Economics
Mathematical Economics

Author: Vasily E. Tarasov

Publisher: MDPI

Published: 2020-06-03

Total Pages: 278

ISBN-13: 303936118X

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This book is devoted to the application of fractional calculus in economics to describe processes with memory and non-locality. Fractional calculus is a branch of mathematics that studies the properties of differential and integral operators that are characterized by real or complex orders. Fractional calculus methods are powerful tools for describing the processes and systems with memory and nonlocality. Recently, fractional integro-differential equations have been used to describe a wide class of economical processes with power law memory and spatial nonlocality. Generalizations of basic economic concepts and notions the economic processes with memory were proposed. New mathematical models with continuous time are proposed to describe economic dynamics with long memory. This book is a collection of articles reflecting the latest mathematical and conceptual developments in mathematical economics with memory and non-locality based on applications of fractional calculus.

American-Type Options
American-Type Options

Author: Dmitrii S. Silvestrov

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2015-03-03

Total Pages: 672

ISBN-13: 3110389908

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The book gives a systematical presentation of stochastic approximation methods for discrete time Markov price processes. Advanced methods combining backward recurrence algorithms for computing of option rewards and general results on convergence of stochastic space skeleton and tree approximations for option rewards are applied to a variety of models of multivariate modulated Markov price processes. The principal novelty of presented results is based on consideration of multivariate modulated Markov price processes and general pay-off functions, which can depend not only on price but also an additional stochastic modulating index component, and use of minimal conditions of smoothness for transition probabilities and pay-off functions, compactness conditions for log-price processes and rate of growth conditions for pay-off functions. The volume presents results on structural studies of optimal stopping domains, Monte Carlo based approximation reward algorithms, and convergence of American-type options for autoregressive and continuous time models, as well as results of the corresponding experimental studies.

The 19th International Conference on Industrial Engineering and Engineering Management
The 19th International Conference on Industrial Engineering and Engineering Management

Author: Ershi Qi

Publisher: Springer Science & Business Media

Published: 2013-06-25

Total Pages: 1596

ISBN-13: 3642384277

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The International Conference on Industrial Engineering and Engineering Management is sponsored by the Chinese Industrial Engineering Institution, CMES, which is the only national-level academic society for Industrial Engineering. The conference is held annually as the major event in this arena. Being the largest and the most authoritative international academic conference held in China, it provides an academic platform for experts and entrepreneurs in the areas of international industrial engineering and management to exchange their research findings. Many experts in various fields from China and around the world gather together at the conference to review, exchange, summarize and promote their achievements in the fields of industrial engineering and engineering management. For example, some experts pay special attention to the current state of the application of related techniques in China as well as their future prospects, such as green product design, quality control and management, supply chain and logistics management to address the need for, amongst other things low-carbon, energy-saving and emission-reduction. They also offer opinions on the outlook for the development of related techniques. The proceedings offers impressive methods and concrete applications for experts from colleges and universities, research institutions and enterprises who are engaged in theoretical research into industrial engineering and engineering management and its applications. As all the papers are of great value from both an academic and a practical point of view, they also provide research data for international scholars who are investigating Chinese style enterprises and engineering management.

Stochastic Calculus for Fractional Brownian Motion and Applications
Stochastic Calculus for Fractional Brownian Motion and Applications

Author: Francesca Biagini

Publisher: Springer Science & Business Media

Published: 2008-02-17

Total Pages: 331

ISBN-13: 1846287979

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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.

Probability Models
Probability Models

Author:

Publisher: Elsevier

Published: 2024-10-24

Total Pages: 828

ISBN-13: 0443293295

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Probability Models, Volume 51 in the Handbook of Statistics series, highlights new advances in the field, with this new volume presenting interesting chapters on Stein's methods, Probabilities and thermodynamics third law, Random Matrix Theory, General tools for understanding fluctuations of random variables, An approximation scheme to compute the Fisher-Rao distance between multivariate normal distributions, Probability Models Applied to Reliability and Availability Engineering, Backward stochastic differential equation– Stochastic optimization theory and viscous solution of HJB equation, and much more.Additional chapters cover Probability Models in Machine Learning, The recursive stochastic algorithm, randomized urn models and response-adaptive randomization in clinical trials, Random matrix theory: local laws and applications, KOO methods and their high-dimensional consistencies in some multivariate models, Fourteen Lectures on Inference for Stochastic Processes, and A multivariate cumulative damage model and some applications. - Provides the latest information on probability models - Offers outstanding and original reviews on a range of probability models research topics - Serves as an indispensable reference for researchers and students alike