| Description |
1 online resource (220 pages) |
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text file |
| Contents |
Abbreviations; Introduction; 1 Random variables and probability distributions; 1.1 Particle descriptions of partial differential equations; 1.2 Random variables and stochastic processes; 1.3 The n-point probability distributions; 1.4 Simple averages and scaling; 1.5 Pair correlations and 2-point densities; 1.6 Conditional probability densities; 1.7 Statistical ensembles and time series; 1.8 When are pair correlations enough to identify a stochastic process?; Additional reading; Exercises; 2 Martingales, Markov, and nonstationarity; 2.1 Statistically independent increments. |
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2.2 Stationary increments2.3 Martingales; 2.4 Nonstationary increment processes; 2.5 Markov processes; 2.6 Drift plus noise; 2.7 Gaussian processes; 2.8 Stationary vs. nonstationary processes; Additional reading; Exercises; 3 Stochastic calculus; 3.1 The Wiener process; 3.2 Ito's theorem; 3.3 Ito's lemma; 3.4 Martingales for greenhorns; 3.5 First-passage times; Additional reading; Exercises; 4 Ito processes and Fokker-Planck equations; 4.1 Stochastic differential equations; 4.2 Ito's lemma; 4.3 The Fokker-Planck pde; 4.4 The Chapman-Kolmogorov equation; 4.5 Calculating averages. |
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4.6 Statistical equilibrium4.7 An ergodic stationary process; 4.8 Early models in statistical physics and finance; 4.9 Nonstationary increments revisited; Additional reading; Exercises; 5 Selfsimilar Ito processes; 5.1 Selfsimilar stochastic processes; 5.2 Scaling in diffusion; 5.3 Superficially nonlinear diffusion; 5.4 Is there an approach to scaling?; 5.5 Multiaffine scaling; Additional reading; Exercises; 6 Fractional Brownian motion; 6.1 Introduction; 6.2 Fractional Brownian motion; 6.3 The distribution of fractional Brownian motion; 6.4 Infinite memory processes. |
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6.5 The minimal description of dynamics6.6 Pair correlations cannot scale; 6.7 Semimartingales; Additional reading; Exercises; 7 Kolmogorov's pdes and Chapman-Kolmogorov; 7.1 The meaning of Kolmogorov's first pde; 7.2 An example of backward-time diffusion; 7.3 Deriving the Chapman-Kolmogorov equation for an Ito process; Additional reading; Exercise; 8 Non-Markov Ito processes; 8.1 Finite memory Ito processes?; 8.2 A Gaussian Ito process with 1-state memory; 8.3 McKean's examples; 8.4 The Chapman-Kolmogorov equation; 8.5 Interacting system with a phase transition. |
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8.6 The meaning of the Chapman-Kolmogorov equationAdditional reading; Exercise; 9 Black-Scholes, martingales, and Feynman-Kac; 9.1 Local approximation to sdes; 9.2 Transition densities via path integrals; 9.3 Black-Scholes-type pdes; Additional reading; Exercise; 10 Stochastic calculus with martingales; 10.1 Introduction; 10.2 Integration by parts; 10.3 An exponential martingale; 10.4 Girsanov's theorem; 10.5 An application of Girsanov's theorem; 10.6 Topological inequivalence of martingales with Wiener processes; 10.7 Solving diffusive pdes by running an Ito process; 10.8 First-passage times. |
| Note |
10.9 Martingales generally seen. |
| Summary |
Provides graduate students and practitioners in physics and economics with a better understanding of stochastic processes. |
| Bibliography |
Includes bibliographical references and index. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Stochastic processes.
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Stochastic processes. |
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Differential equations.
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Differential equations. |
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Statistical physics.
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Statistical physics. |
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Finance -- Mathematical models.
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Finance -- Mathematical models. |
| Genre/Form |
Electronic books.
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| Other Form: |
Print version: McCauley, Joseph L. Stochastic Calculus and Differential Equations for Physics and Finance. Cambridge : Cambridge University Press, ©2013 9780521763400 |
| ISBN |
9781107334571 |
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1107334578 |
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0521763401 |
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9780521763400 |
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9781107326477 |
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1107326478 |
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9781107336230 (electronic book) |
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1107336236 (electronic book) |
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9781299257429 (MyiLibrary) |
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1299257429 (MyiLibrary) |
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9781139019460 (electronic book) |
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1139019465 (electronic book) |
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9781107332911 |
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1107332915 |
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9780521763400 |
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