Stochastic Calculus and Applications

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 work... Ausführliche Beschreibung

1. Person: Cohen, Samuel N.
Weitere Körperschaften: SpringerLink (Online service)
Weitere Personen: Elliott, Robert J. [author]
Format: E-Buch
Sprache: English
Veröffentlicht: New York, NY Springer New York 2015, 2015
Beschreibung: XXIII, 666 p. 17 illus online resource
Ausgabe: 2nd ed. 2015
Serien: Probability and Its Applications
Schlagworte: Probability Theory and Stochastic Processes
Electrical engineering
Computational Mathematics and Numerical Analysis
Partial Differential Equations
Computer mathematics
Economics, Mathematical
Electrical Engineering
Partial differential equations
Quantitative Finance
Mathematics
Probabilities
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100 1 |a Cohen, Samuel N. 
245 0 0 |a Stochastic Calculus and Applications  |h Elektronische Ressource  |c by Samuel N. Cohen, Robert J. Elliott 
250 |a 2nd ed. 2015 
260 |a New York, NY  |b Springer New York  |c 2015, 2015 
300 |a XXIII, 666 p. 17 illus  |b online resource 
505 0 |a Measure Theoretic Probability -- Measure Integral -- Probabilities and Expectation -- Part II: Stochastic Processes -- Filtrations, Stopping Times and Stochastic Processes -- Martingales in Discrete Time -- Martingales in Continuous Time -- The Classification of Stopping Times -- The Progressive, Optional and Predicable -Algebras -- Part III: Stochastic Integration -- Processes of Finite Variation -- The Doob-Meyer Decomposition -- The Structure of Square Integrable Martingales -- Quadratic Variation and Semimartingales -- The Stochastic Integral -- Random Measures -- Part IV: Stochastic Differential Equations -- Ito's Differential Rule -- The Exponential Formula and Girsanov's Theorem -- Lipschitz Stochastic Differential Equations -- Markov Properties of SDEs -- Weak Solutions of SDEs -- Backward Stochastic Differential Equations -- Part V: Applications -- Control of a Single Jump -- Optimal Control of Drifts and Jump Rates -- Filtering. Part VI: Appendices 
653 |a Probability Theory and Stochastic Processes 
653 |a Electrical engineering 
653 |a Computational Mathematics and Numerical Analysis 
653 |a Partial Differential Equations 
653 |a Computer mathematics 
653 |a Economics, Mathematical 
653 |a Electrical Engineering 
653 |a Partial differential equations 
653 |a Quantitative Finance 
653 |a Mathematics 
653 |a Probabilities 
700 1 |a Elliott, Robert J.  |e [author] 
710 2 |a SpringerLink (Online service) 
041 0 7 |a eng  |2 ISO 639-2 
989 |b Springer  |a Springer eBooks 2005- 
490 0 |a Probability and Its Applications 
856 |u http://dx.doi.org/10.1007/978-1-4939-2867-5?nosfx=y  |x Verlag  |3 Volltext 
082 0 |a 519.2 
520 |a 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) 

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