Stochastic processes from physics to finance Wolfgang Paul, Jörg Baschnagel

Format:

Book

Author/Creator:

Paul, Wolfgang, 1959-

Contributor:

Baschnagel, Jörg, 1965-

Language:

English

Subjects (All):

Stochastic processes.

Stochastic Processes.

Medical Subjects:

Stochastic Processes.

Physical Description:

1 online resource

Edition:

2nd ed.

Place of Publication:

Berlin New York Springer ©2013

Summary:

"The book is an introduction to stochastic processes with applications from physics and finance. It introduces the basic notions of probability theory and the mathematics of stochastic processes. The applications that we discuss are chosen to show the interdisciplinary character of the concepts and methods and are taken from physics and finance. Due to its interdisciplinary character and choice of topics, the book can show students and researchers in physics how models and techniques used in their field can be translated into and applied in the field of finance and risk-management. On the other hand, a practitioner from the field of finance will find models and approaches recently developed in the emerging field of econophysics for understanding the stochastic price behavior of financial assets."--Jacket

Contents:

Stochastic Processes; Preface to the Second Edition; Preface to the First Edition; Contents; Chapter 1: A First Glimpse of Stochastic Processes; 1.1 Some History; 1.2 Random Walk on a Line; 1.2.1 From Binomial to Gaussian; 1.2.2 From Binomial to Poisson; 1.2.3 Log-Normal Distribution; 1.3 Further Reading; Section 1.1; Section 1.2; Chapter 2: A Brief Survey of the Mathematics of Probability Theory; 2.1 Some Basics of Probability Theory; 2.1.1 Probability Spaces and Random Variables; 2.1.2 Probability Theory and Logic; Maximum Entropy Approach; Maximum Entropy Approach to Statistical Physics

2.1.3 Equivalent Measures2.1.4 Distribution Functions and Probability Densities; 2.1.5 Statistical Independence and Conditional Probabilities; 2.1.6 Central Limit Theorem; 2.1.7 Extreme Value Distributions; 2.2 Stochastic Processes and Their Evolution Equations; 2.2.1 Martingale Processes; 2.2.2 Markov Processes; Stationary Markov Processes and the Master Equation; Fokker-Planck and Langevin Equations; 2.3 Itô Stochastic Calculus; 2.3.1 Stochastic Integrals; 2.3.2 Stochastic Differential Equations and the Itô Formula; 2.4 Summary; 2.5 Further Reading; Section 2.1; Section 2.2; Section 2.3.

Chapter 3: Diffusion Processes3.1 The Random Walk Revisited; 3.1.1 Polya Problem; 3.1.2 Rayleigh-Pearson Walk; A Polymer Model; 3.1.3 Continuous-Time Random Walk; 3.2 Free Brownian Motion; 3.2.1 Velocity Process; The Velocity Distribution; 3.2.2 Position Process; The Position Distribution; 3.3 Caldeira-Leggett Model; 3.3.1 Definition of the Model; 3.3.2 Velocity Process and Generalized Langevin Equation; 3.4 On the Maximal Excursion of Brownian Motion; 3.5 Brownian Motion in a Potential: Kramers Problem; 3.5.1 First Passage Time for One-dimensional Fokker-Planck Equations; 3.5.2 Kramers Result

3.6 A First Passage Problem for Unbounded Diffusion3.7 Kinetic Ising Models and Monte Carlo Simulations; 3.7.1 Probabilistic Structure; 3.7.2 Monte Carlo Kinetics; 3.7.3 Mean-Field Kinetic Ising Model; 3.8 Quantum Mechanics as a Diffusion Process; 3.8.1 Hydrodynamics of Brownian Motion; 3.8.2 Conservative Diffusion Processes; 3.8.3 Hypothesis of Universal Brownian Motion; Interpretation; 3.8.4 Tunnel Effect; 3.8.5 Harmonic Oscillator and Quantum Fields; 3.9 Summary; 3.10 Further Reading; Section 3.1; Section 3.2; Section 3.5; Section 3.7; Section 3.8.

Chapter 4: Beyond the Central Limit Theorem: Lévy Distributions4.1 Back to Mathematics: Stable Distributions; 4.2 The Weierstrass Random Walk; 4.2.1 Definition and Solution; Solution and Properties; Fractional Diffusion Equation; 4.2.2 Superdiffusive Behavior; Fractal Dimension; 4.2.3 Generalization to Higher Dimensions; Polya's Problem Revisited; 4.3 Fractal-Time Random Walks; 4.3.1 A Fractal-Time Poisson Process; The Kohlrausch Function; 4.3.2 Subdiffusive Behavior; 4.4 A Way to Avoid Diverging Variance: The Truncated Lévy Flight; Illustration; Addendum; 4.5 Summary; 4.6 Further Reading

Notes:

Includes bibliographical references and index

Online resource; title from PDF title page (SpringerLink, viewed July 18, 2013)

Other Format:

Print version Paul, Wolfgang. Stochastic Processes : From Physics to Finance

ISBN:

9783319003276

3319003275

OCLC:

853106886

Access Restriction:

Restricted for use by site license