Stochastic Calculus and Differential Equations for Physics and Finance.
Provides graduate students and practitioners in physics and economics with a better understanding of stochastic processes.
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| Main Author: | |
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge :
Cambridge University Press,
2013.
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| Subjects: | |
| Online Access: | CONNECT |
MARC
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| 100 | 1 | |a McCauley, Joseph L. | |
| 245 | 1 | 0 | |a Stochastic Calculus and Differential Equations for Physics and Finance. |
| 260 | |a Cambridge : |b Cambridge University Press, |c 2013. | ||
| 300 | |a 1 online resource (220 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 347 | |a data file |2 rda | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 500 | |a 10.9 Martingales generally seen. | ||
| 520 | |a Provides graduate students and practitioners in physics and economics with a better understanding of stochastic processes. | ||
| 504 | |a Includes bibliographical references and index. | ||
| 500 | |a EBSCO eBook Academic Comprehensive Collection North America |5 TMurS | ||
| 650 | 0 | |a Stochastic processes. | |
| 650 | 0 | |a Differential equations. | |
| 650 | 0 | |a Statistical physics. | |
| 650 | 0 | |a Finance |x Mathematical models. | |
| 730 | 0 | |a WORLDSHARE SUB RECORDS | |
| 758 | |i has work: |a Stochastic Calculus and Differential Equations for Physics and Finance (Text) |1 https://id.oclc.org/worldcat/entity/E39PCFvPDjXCmFFpQxvPWBWQRq |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a McCauley, Joseph L. |t Stochastic Calculus and Differential Equations for Physics and Finance. |d Cambridge : Cambridge University Press, ©2013 |z 9780521763400 |
| 856 | 4 | 0 | |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=539283&authtype=ip,sso&custid=s4672406 |z CONNECT |3 eBooks on EBSCOhost |t 0 |
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| 952 | f | f | |a Middle Tennessee State University |b Main |c James E. Walker Library |d Electronic Resources |t 0 |e QC20.7.S8 M39 2012 |h Library of Congress classification |
