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An Informal Introduction To Stochastic Calculus With Applications

Author: Ovidiu Calin
Publisher: World Scientific
ISBN: 9814678953
Size: 46.26 MB
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The goal of this book is to present Stochastic Calculus at an introductory level and not at its maximum mathematical detail. The author aims to capture as much as possible the spirit of elementary deterministic Calculus, at which students have been already exposed. This assumes a presentation that mimics similar properties of deterministic Calculus, which facilitates understanding of more complicated topics of Stochastic Calculus. Contents:A Few Introductory ProblemsBasic NotionsUseful Stochastic ProcessesProperties of Stochastic ProcessesStochastic IntegrationStochastic DifferentiationStochastic Integration TechniquesStochastic Differential EquationsApplications of Brownian MotionGirsanov's Theorem and Brownian MotionSome Applications of Stochastic CalculusHints and Solutions Readership: Undergraduate and graduate students interested in stochastic processes. Key Features:The book contains numerous problems with full solutions and plenty of worked out examples and figures, which facilitate material understandingThe material was tested on students at several universities around the world (Taiwan, Kuwait, USA); this led to a presentation form that balances both technicality and understandingThe presentation mimics as close as possible the same chapters as in deterministic calculus; former calculus students will find this chronology of ideas familiar to CalculusKeywords:Stochastic Processes;Probability Distribution;Brownian Motion;Filtering Theory;Martingale;Ito Calculus;Poisson Process;Bessel Process

Wahrscheinlichkeitstheorie Und Stochastische Prozesse

Author: Michael Mürmann
Publisher: Springer-Verlag
ISBN: 364238160X
Size: 77.76 MB
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Dieses Lehrbuch beschäftigt sich mit den zentralen Gebieten einer maßtheoretisch orientierten Wahrscheinlichkeitstheorie im Umfang einer zweisemestrigen Vorlesung. Nach den Grundlagen werden Grenzwertsätze und schwache Konvergenz behandelt. Es folgt die Darstellung und Betrachtung der stochastischen Abhängigkeit durch die bedingte Erwartung, die mit der Radon-Nikodym-Ableitung realisiert wird. Sie wird angewandt auf die Theorie der stochastischen Prozesse, die nach der allgemeinen Konstruktion aus der Untersuchung von Martingalen und Markov-Prozessen besteht. Neu in einem Lehrbuch über allgemeine Wahrscheinlichkeitstheorie ist eine Einführung in die stochastische Analysis von Semimartingalen auf der Grundlage einer geeigneten Stetigkeitsbedingung mit Anwendungen auf die Theorie der Finanzmärkte. Das Buch enthält zahlreiche Übungen, teilweise mit Lösungen. Neben der Theorie vertiefen Anmerkungen, besonders zu mathematischen Modellen für Phänomene der Realität, das Verständnis.​

Introduction To Stochastic Processes

Author: Gregory F. Lawler
Publisher: CRC Press
ISBN: 9780412995118
Size: 23.94 MB
Format: PDF, ePub
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This concise, informal introduction to stochastic processes evolving with time was designed to meet the needs of graduate students not only in mathematics and statistics, but in the many fields in which the concepts presented are important, including computer science, economics, business, biological science, psychology, and engineering. With emphasis on fundamental mathematical ideas rather than proofs or detailed applications, the treatment introduces the following topics: Markov chains, with focus on the relationship between the convergence to equilibrium and the size of the eigenvalues of the stochastic matrix Infinite state space, including the ideas of transience, null recurrence and positive recurrence The three main types of continual time Markov chains and optimal stopping of Markov chains Martingales, including conditional expectation, the optional sampling theorem, and the martingale convergence theorem Renewal process and reversible Markov chains Brownian motion, both multidimensional and one-dimensional Introduction to Stochastic Processes is ideal for a first course in stochastic processes without measure theory, requiring only a calculus-based undergraduate probability course and a course in linear algebra.

Deterministic And Stochastic Topics In Computational Finance

Author: Ovidiu Calin
Publisher: World Scientific Publishing Company
ISBN: 9813203102
Size: 39.43 MB
Format: PDF, Docs
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What distinguishes this book from other texts on mathematical finance is the use of both probabilistic and PDEs tools to price derivatives for both constant and stochastic volatility models, by which the reader has the advantage of computing explicitly a large number of prices for European, American and Asian derivatives. The book presents continuous time models for financial markets, starting from classical models such as Black–Scholes and evolving towards the most popular models today such as Heston and VAR. A key feature of the textbook is the large number of exercises, mostly solved, which are designed to help the reader to understand the material. The book is based on the author's lectures on topics on computational finance for senior and graduate students, delivered in USA (Princeton University and EMU), Taiwan and Kuwait. The prerequisites are an introductory course in stochastic calculus, as well as the usual calculus sequence. The book is addressed to undergraduate and graduate students in Masters of Finance programs as well as to those who wish to become more efficient in their practical applications. Topics covered: Interest Rates and BondsForward Rates and Yield CurvesRisk-neutral ValuationMartingale MeasuresBlack–Scholes AnalysisAmerican OptionsStochastic Volatility Models (Heston, AR, GARCH)Stochastic Return Models (VAR) Request Inspection Copy

Mathematik Und Technologie

Author: Christiane Rousseau
Publisher: Springer-Verlag
ISBN: 3642300928
Size: 24.35 MB
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Zusammen mit der Abstraktion ist die Mathematik das entscheidende Werkzeug für technologische Innovationen. Das Buch bietet eine Einführung in zahlreiche Anwendungen der Mathematik auf dem Gebiet der Technologie. Meist werden moderne Anwendungen dargestellt, die heute zum Alltag gehören. Die mathematischen Grundlagen für technologische Anwendungen sind dabei relativ elementar, was die Leistungsstärke der mathematischen Modellbildung und der mathematischen Hilfsmittel beweist. Mit zahlreichen originellen Übungen am Ende eines jeden Kapitels.

Kalman Bucy Filter

Author: Karl Brammer
Publisher:
ISBN:
Size: 64.18 MB
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Das Buch will die mannigfaltigen Aufgaben der heutigen Regelungs- und Steuerungstechnik und ihre Lösung nahebringen. Das soll mit möglichst geringem Zeit- und Arbeitsaufwand für den Leser verbunden sein. Leichte Verständlichkeit, Anschaulichkeit und Anwendungsnähe sind deshalb Hauptgesichtspunkt der Darstellung. Vollständigkeit ist nicht angestrebt, vielmehr Darstellung des Wesentlichen. Mathematische Methoden werden auf das Notwendige beschränkt.

Introduction To Probability And Stochastic Processes With Applications

Author: Liliana Blanco Castañeda
Publisher: John Wiley & Sons
ISBN: 1118344960
Size: 19.70 MB
Format: PDF
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An easily accessible, real-world approach to probability andstochastic processes Introduction to Probability and Stochastic Processes withApplications presents a clear, easy-to-understand treatment ofprobability and stochastic processes, providing readers with asolid foundation they can build upon throughout their careers. Withan emphasis on applications in engineering, applied sciences,business and finance, statistics, mathematics, and operationsresearch, the book features numerous real-world examples thatillustrate how random phenomena occur in nature and how to useprobabilistic techniques to accurately model these phenomena. The authors discuss a broad range of topics, from the basicconcepts of probability to advanced topics for further study,including Itô integrals, martingales, and sigma algebras.Additional topical coverage includes: Distributions of discrete and continuous random variablesfrequently used in applications Random vectors, conditional probability, expectation, andmultivariate normal distributions The laws of large numbers, limit theorems, and convergence ofsequences of random variables Stochastic processes and related applications, particularly inqueueing systems Financial mathematics, including pricing methods such asrisk-neutral valuation and the Black-Scholes formula Extensive appendices containing a review of the requisitemathematics and tables of standard distributions for use inapplications are provided, and plentiful exercises, problems, andsolutions are found throughout. Also, a related website featuresadditional exercises with solutions and supplementary material forclassroom use. Introduction to Probability and StochasticProcesses with Applications is an ideal book for probabilitycourses at the upper-undergraduate level. The book is also avaluable reference for researchers and practitioners in the fieldsof engineering, operations research, and computer science whoconduct data analysis to make decisions in their everyday work.