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EBOOK
Author Hassler, Uwe,
Title Stochastic processes and calculus : an elementary introduction with applications / Uwe Hassler.
Imprint Cham : Springer, [2016]
2016

LOCATION CALL # STATUS MESSAGE
 OHIOLINK SPRINGER EBOOKS    ONLINE  
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LOCATION CALL # STATUS MESSAGE
 OHIOLINK SPRINGER EBOOKS    ONLINE  
View online
Author Hassler, Uwe,
Series Springer texts in business and economics, 2192-4341
Springer texts in business and economics. 2192-4333
Subject Economics, Mathematical -- Textbooks.
Stochastic processes -- Textbooks.
Stochastic models -- Textbooks.
Stochastic integrals -- Textbooks.
Description 1 online resource (xviii, 391 pages) : illustrations (some color).
Bibliography Note Includes bibliographical references and index.
Contents 1. Introduction ; 1.1. Summary ; 1.2. Finance ; 1.3. Econometrics ; 1.4. Mathematics ; 1.5. Problems and Solutions -- PART I. TIME SERIES MODELING ; 2. Basic Concepts from Probability Theory ; 2.1. Summary ; 2.2. Random Variables ; 2.3. Joint and Conditional Distributions ; 2.4. Stochastic Processes (SP) ; 2.5. Problems and Solutions -- 3. AutoregressiveMoving Average Processes (ARMA) ; 3.1. Summary ; 3.2. Moving Average Processes ; 3.3. Lag Polynomials and Invertibility ; 3.4. Autoregressive and Mixed Processes ; 3.5. Problems and Solutions -- 4. Spectra of Stationary Processes ; 4.1. Summary ; 4.2. Definition and Interpretation ; 4.3. Filtered Processes ; 4.4. Examples of ARMA Spectra ; 4.5. Problems and Solutions -- 5. Long Memory and Fractional Integration ; 5.1. Summary ; 5.2. Persistence and Long Memory ; 5.3. Fractionally Integrated Noise ; 5.4. Generalizations ; 5.5. Problems and Solutions -- 6. Processes with Autoregressive Conditional ; Heteroskedasticity (ARCH) ; 6.1. Summary ; 6.2. Time-Dependent Heteroskedasticity ; 6.3. ARCH Models ; 6.4. Generalizations ; 6.5. Problems and Solutions.
PART II. STOCHASTIC INTEGRALS ; 7. Wiener Processes (WP) ; 7.1. Summary ; 7.2. From RandomWalk to Wiener Process ; 7.3. Properties ; 7.4. Functions of Wiener Processes ; 7.5. Problems and Solutions -- 8. Riemann Integrals ; 8.1. Summary ; 8.2. Definition and Fubini's Theorem ; 8.3. Riemann Integration of Wiener Processes ; 8.4. Convergence in Mean Square ; 8.5. Problems and Solutions -- 9. Stieltjes Integrals ; 9.1. Summary ; 9.2. Definition and Partial Integration ; 9.3. Gaussian Distribution and Autocovariances ; 9.4. Standard Ornstein-Uhlenbeck Process ; 9.5. Problems and Solutions -- 10. Ito Integrals ; 10.1. Summary ; 10.2. A Special Case ; 10.3. General Ito Integrals ; 10.4. (Quadratic) Variation ; 10.5. Problems and Solutions -- 11. Ito's Lemma ; 11.1. Summary ; 11.2. The Univariate Case ; 11.3. Bivariate Diffusions with One WP ; 11.4. Generalization for Independent WP ; 11.5. Problems and Solutions.
PART III. APPLICATIONS ; 12. Stochastic Differential Equations (SDE) ; 12.1. Summary ; 12.2. Definition and Existence ; 12.3. Linear Stochastic Differential Equations ; 12.4. Numerical Solutions ; 12.5. Problems and Solutions -- 13. Interest Rate Models ; 13.1. Summary ; 13.2. Ornstein-Uhlenbeck Process (OUP) ; 13.3. Positive Linear Interest Rate Models ; 13.4. Nonlinear Models ; 13.5. Problems and Solutions -- 14. Asymptotics of Integrated Processes ; 14.1. Summary ; 14.2. Limiting Distributions of Integrated Processes ; 14.3. Weak Convergence of Functions ; 14.4. Multivariate Limit Theory ; 14.5. Problems and Solutions -- 15. Trends, Integration Tests and Nonsense Regressions ; 15.1. Summary ; 15.2. Trend Regressions ; 15.3. Integration Tests ; 15.4. Nonsense Regression ; 15.5. Problems and Solutions ; 16. Cointegration Analysis ; 16.1. Summary ; 16.2. Error-Correction and Cointegration ; 16.3. Cointegration Regressions ; 16.4. Cointegration Testing ; 16.5. Problems and Solutions.
Summary "This textbook gives a comprehensive introduction to stochastic processes and calculus in the fields of finance and economics, more specifically mathematical finance and time series econometrics. Over the past decades stochastic calculus and processes have gained great importance, because they play a decisive role in the modeling of financial markets and as a basis for modern time series econometrics. Mathematical theory is applied to solve stochastic differential equations and to derive limiting results for statistical inference on nonstationary processes. This introduction is elementary and rigorous at the same time. On the one hand it gives a basic and illustrative presentation of the relevant topics without using many technical derivations. On the other hand many of the procedures are presented at a technically advanced level: for a thorough understanding, they are to be proven. In order to meet both requirements jointly, the present book is equipped with a lot of challenging problems at the end of each chapter as well as with the corresponding detailed solutions. Thus the virtual text--augmented with more than 60 basic examples and 40 illustrative figures--is rather easy to read while a part of the technical arguments is transferred to the exercise problems and their solutions."--Publisher's description
ISBN 9783319234281 (electronic bk.)
3319234285 (electronic bk.)
3319234277
9783319234274
ISBN/ISSN 9783319234274
10.1007/978-3-319-23428-1
OCLC # 936352645
Additional Format Print version: Hassler, Uwe. Stochastic processes and calculus. Cham : Springer, [2016] 3319234277 (DLC) 2015957196 (OCoLC)915119938


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