Stochastic Integration and Stochastic Differential Equations
by Klaus Bichteler
Publisher: University of Texas 2002
Number of pages: 643
Written for graduate students of mathematics, physics, electrical engineering, and finance. The students are expected to know the basics of point set topology up to Tychonoff's theorem, general integration theory, and enough functional analysis to recognize the Hahn-Banach theorem.
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by O. Melchert - arXiv
In these lecture notes, a selection of frequently required statistical tools will be introduced and illustrated. They allow to post-process data that stem from, e.g., large-scale numerical simulations (aka sequence of random experiments).
by J. C. Lemm - arXiv.org
A particular Bayesian field theory is defined by combining a likelihood model, providing a probabilistic description of the measurement process, and a prior model, providing the information necessary to generalize from training to non-training data.
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The first part deals with discrete inverse problems with a finite number of parameters, while the second part deals with general inverse problems. The book for scientists and applied mathematicians facing the interpretation of experimental data.
by Thomas G. Kurtz - University of Wisconsin
Covered topics: stochastic integrals with respect to general semimartingales, stochastic differential equations based on these integrals, integration with respect to Poisson measures, stochastic differential equations for general Markov processes.