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This graduate level text covers the theory of stochastic integration, an important area of Mathematics with a wide range of applications, including financial mathematics and signal processing.

Stochastic integrals. --- Martingales (Mathematics) --- Stochastic processes. --- Random processes --- Probabilities --- Stochastic processes --- Integrals, Stochastic --- Stochastic analysis

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This book provides an introductory albeit solid presentation of path integration techniques as applied to the field of stochastic processes. The subject began with the work of Wiener during the 1920's, corresponding to a sum over random trajectories, anticipating by two decades Feynman's famous work on the path integral representation of quantum mechanics. However, the true trigger for the application of these techniques within nonequilibrium statistical mechanics and stochastic processes was the work of Onsager and Machlup in the early 1950's. The last quarter of the 20th century has witnesse

Function spaces. --- Stochastic integrals. --- Integrals, Stochastic --- Stochastic analysis --- Spaces, Function --- Functional analysis --- Stochastic processes. --- Path integrals.

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Ordinary differential equations --- Stochastic processes --- Differentiaalvergelijkingen [Stochastische ] --- Equations differentielles stochastiques --- Integralen [Stochastische ] --- Integrales stochastiques --- Integrals [Stochastic ] --- Martingalen (Wiskunde) --- Martingales (Mathematics) --- Martingales (Mathematiques) --- Stochastic differential equations --- Stochastic integrals --- Martingales (Mathématiques) --- Equations différentielles stochastiques --- 519.217 --- Markov processes --- 519.217 Markov processes --- Martingales (Mathématiques) --- Equations différentielles stochastiques --- Differential equations --- Fokker-Planck equation --- Integrals, Stochastic --- Stochastic analysis

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Stochastic processes --- Martingales (Mathematics) --- Decomposition (Mathematics) --- 519.216 --- Stochastic integrals --- #WWIS:STAT --- Integrals, Stochastic --- Stochastic analysis --- Mathematics --- Probabilities --- Stochastic processes in general. Prediction theory. Stopping times. Martingales --- 519.216 Stochastic processes in general. Prediction theory. Stopping times. Martingales

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The theory of stochastic integration, also called the Ito calculus, has a large spectrum of applications in virtually every scientific area involving random functions, but it can be a very difficult subject for people without much mathematical background. The Ito calculus was originally motivated by the construction of Markov diffusion processes from infinitesimal generators. Previously, the construction of such processes required several steps, whereas Ito constructed these diffusion processes directly in a single step as the solutions of stochastic integral equations associated with the infinitesimal generators. Moreover, the properties of these diffusion processes can be derived from the stochastic integral equations and the Ito formula. This introductory textbook on stochastic integration provides a concise introduction to the Ito calculus, and covers the following topics: * Constructions of Brownian motion; * Stochastic integrals for Brownian motion and martingales; * The Ito formula; * Multiple Wiener-Ito integrals; * Stochastic differential equations; * Applications to finance, filtering theory, and electric circuits. The reader should have a background in advanced calculus and elementary probability theory, as well as a basic knowledge of measure theory and Hilbert spaces. Each chapter ends with a variety of exercises designed to help the reader further understand the material. Hui-Hsiung Kuo is the Nicholson Professor of Mathematics at Louisiana State University. He has delivered lectures on stochastic integration at Louisiana State University, Cheng Kung University, Meijo University, and University of Rome "Tor Vergata," among others. He is also the author of Gaussian Measures in Banach Spaces (Springer 1975), and White Noise Distribution Theory (CRC Press 1996), and a memoir of his childhood growing up in Taiwan, An Arrow Shot into the Sun (Abridge Books 2004).

Mathematics. --- Economics, Mathematical. --- Probabilities. --- Probability Theory and Stochastic Processes. --- Quantitative Finance. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Economics --- Mathematical economics --- Econometrics --- Math --- Science --- Methodology --- Stochastic integrals. --- Martingales (Mathematics) --- Stochastic processes --- Integrals, Stochastic --- Stochastic analysis --- Distribution (Probability theory. --- Finance. --- Funding --- Funds --- Currency question --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Economics, Mathematical .