An Introduction to Stochastic PDEs
by Martin Hairer
Publisher: arXiv 2009
Number of pages: 78
This text is an attempt to give a reasonably self-contained presentation of the basic theory of stochastic partial differential equations, taking for granted basic measure theory, functional analysis and probability theory, but nothing else.
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by Cosma Rohilla Shalizi
Contents: Probability (Probability Calculus, Random Variables, Discrete and Continuous Distributions); Statistics (Handling of Data, Sampling, Estimation, Hypothesis Testing); Stochastic Processes (Markov Processes, Continuous-Time Processes).
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Triggered by a recent interesting article on the too frequent incorrect use of probabilistic evidence in courts, the author introduces the basic concepts of probabilistic inference with a toy model, and discusses several important issues.
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The book covers broad areas such as topologic and combinatorial aspects of random matrix theory; scaling limits, universalities and phase transitions in matrix models; universalities for random polynomials; and applications to integrable systems.
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Topics: Data Analysis; Probability; Random Variables and Discrete Distributions; Continuous Probability Distributions; Sampling Distributions; Point and Interval Estimation; Large Sample Estimation; Large-Sample Tests of Hypothesis; etc.