Brownian motion and stochastic calculus

Name: Brownian motion and stochastic calculus
ISBN: 0387976558

by Ioannis Karatzas, Steven E. Shreve · first published 1988

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Data & Statistics Mathematics

This book is designed for a graduate course in stochastic processes. It is written for the reader who is familiar with measure-theoretic probability and the theory of discrete-time processes who is now ready to explore continuous-time stochastic processes. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a Markov process and a martingale in continuous time. The authors show how, by means of stochastic integration and random time change, all continuous martingales and many continuous Markov processes can be represented in terms of Br

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veyron · Oct 31, 2011 · Recommends

…- "Introduction to Stochastic Calculus Applied to Finance" by Lamberton and Lapeyre (Nice little intro) - "Arbitrage Theory in Continuous Time" by Tomas Bjork (Slower discussion, larger breadth) - "Brownian Motion and Stochastic Calculus" and "Methods of Mathematical Finance" by Karatzas and Shreve (Solid theoretical foundation, for the more mathematically inclined) There was a good non-measure theoretic discussion of financial models…
on “Good books for hackers interested in quant finance?” ↗
graycat · Jul 8, 2018 · Recommends

…Breiman's Probability is easier to read than Neveu. So, is K. L. Chung's competitive book. And there are others. There is some more advanced material, e.g., Ioannis Karatzas and Steven E.\ Shreve, {\it Brownian Motion and Stochastic Calculus, Second Edition,\/} Good luck!
on “Ask HN: What are your favorite statistics and probability textbooks?” ↗
HilbertSpace · Oct 4, 2010 · Recommends

…Poisson process and the main convergence theorem in finite Markov chains (also a linear algebra result). Then for more, note again the relevant sections of Breiman and Loeve and then: Karatzas and Shreve, Brownian Motion and Stochastic Calculus.
on “Ask HN: Learning advanced math” ↗
graycat · Dec 4, 2014 · Recommends

…etc. Now will be able to understand EE treatments of second order stationary stochastic processes, digital filtering, power spectral estimation, etc. Stochastic processes, e.g., Karatzas and Shreve. Brownian Motion and Stochastic Calculus. Now can get started on mathematical finance. But there are many side trips available in numerical methods, linear programming, Lagrange multipliers (a surprisingly general technique), integer programming (a…
on “Ask HN: How or where to begin learning mathematics from first principles?” ↗
graycat · Sep 17, 2019 · Recommends

…Loeve students. Can use this work to make good sense out of Brownian motion, and there are plenty of books there. And can do more on stochastic processes, e.g., Ioannis Karatzas and Steven E. Shreve, Brownian Motion and Stochastic Calculus. R. S. Lipster and A. N. Shiryayev, Statistics of Random Processes. Ronald K. Getoor, Markov Processes and Potential Theory. This material is now decades old. With this material it is possible to give…
on “Gaussian Processes, not quite for dummies” ↗
graycat · Dec 28, 2021 · Mentions

…prerequisites of measure theory with sigma algebras, Markov processes, Brownian motion, the Radon-Nikodym theorem, conditional expectation, stochastic integration, e.g., Ioannis Karatzas, Steven E. Shreve, Brownian Motion and Stochastic Calculus, Robert M. Blumenthal and Ronald K. Getoor, Markov Processes and Potential Theory. Can also want parabolic partial differential equations and stochastic dynamic programming. In my experience, with a…
on “‘Hard’ skills from PhDs remain relevant beyond academia” ↗
kurtosis · May 28, 2008 · Mentions

…that Persi Diaconis (of the seven shuffles theorem fame) was motivated to finish high school after dropping out so that he could understand the contents of this book. 'nuff said. Karatzas and Shreve "Brownian Motion and Stochastic Calculus" is also a popular book among quants.
on “Ask YC: Best book to learns statistics?” ↗
jeffwass · Dec 30, 2015 · Mentions

FYI, Shreve's "Brownian Motion and Stochastic Calculus" book is available : http://link.springer.com/book/10.1007/978-1-4684-0302-2
on “Springer Textbooks More Than 10 Years Old Available for Free Legal Download” ↗
NY_USA_Hacker · Mar 20, 2011 · Mentions

…Walter Rudin, 'Real and Complex Analysis', ISBN 07-054232-5, McGraw-Hill. This approach to probability is the one used in essentially all advanced work, e.g., Ioannis Karatzas and Steven E. Shreve, 'Brownian Motion and Stochastic Calculus, Second Edition', ISBN 0-387-97655-8. Jean-Rene Barra, 'Mathematical Basis of Statistics', ISBN 0-12-079240-0, Academic Press. Early in Neveu can see some ways we get essentially pushed into this foundation…
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graycat · Oct 3, 2015 · Mentions

…time can be a bit of a challenge. That topic can be important, e.g., for Brownian motion and stochastic differential equations used in mathematical finance. Of course, there is Karatzas and Shreve, Brownian Motion and Stochastic Calculus and Chung and Williams, Introduction to Stochastic Integration. And there's much more, especially from Russia and France. But, otherwise, usually in practice, what people are interested in is either (1)…
on “Foundations of probability theory” ↗