Stochastic Processes And Calculus Explained

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Stochastic Processes And Calculus Explained

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Author : Vikas Rathi
language : en
Publisher: Educohack Press
Release Date : 2025-02-20

Stochastic Processes And Calculus Explained written by Vikas Rathi and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.

"Stochastic Processes and Calculus Explained" is an essential textbook designed to help readers understand and apply stochastic processes across various fields. Written in clear, accessible language, this book provides a solid foundation in probability theory and calculus while diving into stochastic processes, including random variables, probability distributions, Brownian motion, stochastic integration, and stochastic differential equations. We emphasize the practical relevance of these concepts in finance, physics, engineering, and biology. Our guide illustrates how stochastic processes model uncertainty and randomness, aiding in informed decision-making, outcome prediction, and complex system analysis. With real-world examples and exercises, we ensure readers can grasp and apply these concepts effectively. The book offers a strong mathematical foundation, covering key tools and techniques such as probability theory, calculus, and linear algebra, essential for understanding stochastic processes. Catering to readers of all backgrounds and expertise levels, "Stochastic Processes and Calculus Explained" is ideal for beginners and experienced practitioners alike. Its clear explanations, intuitive coverage, and comprehensive approach make it an invaluable resource for students, researchers, and professionals worldwide.

Stochastic Calculus And Applications

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Author : Samuel N. Cohen
language : en
Publisher: Birkhäuser
Release Date : 2015-11-18

Stochastic Calculus And Applications written by Samuel N. Cohen and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-18 with Mathematics categories.

Completely revised and greatly expanded, the new edition of this text takes readers who have been exposed to only basic courses in analysis through the modern general theory of random processes and stochastic integrals as used by systems theorists, electronic engineers and, more recently, those working in quantitative and mathematical finance. Building upon the original release of this title, this text will be of great interest to research mathematicians and graduate students working in those fields, as well as quants in the finance industry. New features of this edition include: End of chapter exercises; New chapters on basic measure theory and Backward SDEs; Reworked proofs, examples and explanatory material; Increased focus on motivating the mathematics; Extensive topical index. "Such a self-contained and complete exposition of stochastic calculus and applications fills an existing gap in the literature. The book can be recommended for first-year graduate studies. It will be useful for all who intend to work with stochastic calculus as well as with its applications."–Zentralblatt (from review of the First Edition)

Introduction To Stochastic Calculus With Applications 3rd Edition

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Author : Fima C Klebaner
language : en
Publisher: World Scientific Publishing Company
Release Date : 2012-03-21

Introduction To Stochastic Calculus With Applications 3rd Edition written by Fima C Klebaner and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-21 with Mathematics categories.

This book presents a concise and rigorous treatment of stochastic calculus. It also gives its main applications in finance, biology and engineering. In finance, the stochastic calculus is applied to pricing options by no arbitrage. In biology, it is applied to populations' models, and in engineering it is applied to filter signal from noise. Not everything is proved, but enough proofs are given to make it a mathematically rigorous exposition.This book aims to present the theory of stochastic calculus and its applications to an audience which possesses only a basic knowledge of calculus and probability. It may be used as a textbook by graduate and advanced undergraduate students in stochastic processes, financial mathematics and engineering. It is also suitable for researchers to gain working knowledge of the subject. It contains many solved examples and exercises making it suitable for self study.In the book many of the concepts are introduced through worked-out examples, eventually leading to a complete, rigorous statement of the general result, and either a complete proof, a partial proof or a reference. Using such structure, the text will provide a mathematically literate reader with rapid introduction to the subject and its advanced applications. The book covers models in mathematical finance, biology and engineering. For mathematicians, this book can be used as a first text on stochastic calculus or as a companion to more rigorous texts by a way of examples and exercises./a

It S Stochastic Calculus And Probability Theory

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

It S Stochastic Calculus And Probability Theory written by Nobuyuki Ikeda 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.

Professor Kiyosi Ito is well known as the creator of the modern theory of stochastic analysis. Although Ito first proposed his theory, now known as Ito's stochastic analysis or Ito's stochastic calculus, about fifty years ago, its value in both pure and applied mathematics is becoming greater and greater. For almost all modern theories at the forefront of probability and related fields, Ito's analysis is indispensable as an essential instrument, and it will remain so in the future. For example, a basic formula, called the Ito formula, is well known and widely used in fields as diverse as physics and economics. This volume contains 27 papers written by world-renowned probability theorists. Their subjects vary widely and they present new results and ideas in the fields where stochastic analysis plays an important role. Also included are several expository articles by well-known experts surveying recent developments. Not only mathematicians but also physicists, biologists, economists and researchers in other fields who are interested in the effectiveness of stochastic theory will find valuable suggestions for their research. In addition, students who are beginning their study and research in stochastic analysis and related fields will find instructive and useful guidance here. This volume is dedicated to Professor Ito on the occasion of his eightieth birthday as a token of deep appreciation for his great achievements and contributions. An introduction to and commentary on the scientific works of Professor Ito are also included.

Introduction To Stochastic Analysis And Malliavin Calculus

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Author : Jai Rathod
language : en
Publisher:
Release Date : 2015-08

Introduction To Stochastic Analysis And Malliavin Calculus written by Jai Rathod and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08 with categories.

Stochastic calculus is a branch of mathematics that operates on stochastic processes. It allows a consistent theory of integration to be defined for integrals of stochastic processes with respect to stochastic processes. It is used to model systems that behave randomly. The best-known stochastic process to which stochastic calculus is applied is the Wiener process, the Wiener process has been widely applied in financial mathematics and economics to model the evolution in time of stock prices and bond interest rates. The Malliavin calculus extends the calculus of variations from functions to stochastic processes. The Malliavin calculus is also called the stochastic calculus of variations. In particular, it allows the computation of derivatives of random variables. Malliavin's ideas led to a proof that H�rmander's condition implies the existence and smoothness of a density for the solution of a stochastic differential equation; H�rmander's original proof was based on the theory of partial differential equations. The calculus has been applied to stochastic partial differential equations as well. The calculus allows integration by parts with random variables; this operation is used in mathematical finance to compute the sensitivities of financial derivatives. The calculus has applications in, for example, stochastic filtering. This book emphasizes on differential stochastic equations and Malliavin calculus.

Stochastic Analysis

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Author : Hiroyuki Matsumoto
language : en
Publisher: Cambridge University Press
Release Date : 2017

Stochastic Analysis written by Hiroyuki Matsumoto 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 2017 with Mathematics categories.

Developing the Itô calculus and Malliavin calculus in tandem, this book crystallizes modern day stochastic analysis into a single volume.

Stochastic Calculus

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Author : Richard Durrett
language : en
Publisher: CRC Press
Release Date : 2018-03-29

Stochastic Calculus written by Richard Durrett and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-29 with Mathematics categories.

This compact yet thorough text zeros in on the parts of the theory that are particularly relevant to applications . It begins with a description of Brownian motion and the associated stochastic calculus, including their relationship to partial differential equations. It solves stochastic differential equations by a variety of methods and studies in detail the one-dimensional case. The book concludes with a treatment of semigroups and generators, applying the theory of Harris chains to diffusions, and presenting a quick course in weak convergence of Markov chains to diffusions. The presentation is unparalleled in its clarity and simplicity. Whether your students are interested in probability, analysis, differential geometry or applications in operations research, physics, finance, or the many other areas to which the subject applies, you'll find that this text brings together the material you need to effectively and efficiently impart the practical background they need.

Stochastic Calculus For Fractional Brownian Motion And Related Processes

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Author : Yuliya Mishura
language : en
Publisher: Springer
Release Date : 2008-04-12

Stochastic Calculus For Fractional Brownian Motion And Related Processes written by Yuliya Mishura and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-12 with Mathematics categories.

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.

Stochastic Calculus Of Variations

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Author : Yasushi Ishikawa
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2016-03-07

Stochastic Calculus Of Variations written by Yasushi Ishikawa and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-07 with Mathematics categories.

This monograph is a concise introduction to the stochastic calculus of variations (also known as Malliavin calculus) for processes with jumps. It is written for researchers and graduate students who are interested in Malliavin calculus for jump processes. In this book "processes with jumps" includes both pure jump processes and jump-diffusions. The author provides many results on this topic in a self-contained way; this also applies to stochastic differential equations (SDEs) "with jumps". The book also contains some applications of the stochastic calculus for processes with jumps to the control theory and mathematical finance. Namely, asymptotic expansions functionals related with financial assets of jump-diffusion are provided based on the theory of asymptotic expansion on the Wiener–Poisson space. Solving the Hamilton–Jacobi–Bellman (HJB) equation of integro-differential type is related with solving the classical Merton problem and the Ramsey theory. The field of jump processes is nowadays quite wide-ranging, from the Lévy processes to SDEs with jumps. Recent developments in stochastic analysis have enabled us to express various results in a compact form. Up to now, these topics were rarely discussed in a monograph. Contents: Preface Preface to the second edition Introduction Lévy processes and Itô calculus Perturbations and properties of the probability law Analysis of Wiener–Poisson functionals Applications Appendix Bibliography List of symbols Index

Stochastic Calculus

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Author : Mircea Grigoriu
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-09-24

Stochastic Calculus written by Mircea Grigoriu 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 2002-09-24 with Mathematics categories.

Chapters 6-9 present methods for solving problems defined by equations with deterministic and/or random coefficients and deterministic and/or stochastic inputs. The Monte Carlo simulation is used extensively throughout to clarify advanced theoretical concepts and provide solutions to a broad range of stochastic problems.".