by David Nualart
Publisher: Universitat de Barcelona 2003
Number of pages: 148
From the table of contents: Stochastic Processes (Probability Spaces and Random Variables, Definitions and Examples); Jump Processes (The Poisson Process, Superposition of Poisson Processes); Markov Chains; Martingales; Stochastic Calculus.
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by Gane Samb Lo - arXiv.org
The fundamental aspects of Probability Theory are presented from a pure mathematical view based on Measure Theory. Such an approach places Probability Theory in its natural frame of Functional Analysis and offers a basis towards Statistics Theory.
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A self-contained treatment of the theory of probability, random processes. It is intended to lay theoretical foundations for measure and integration theory, and to develop the long term time average behavior of measurements made on random processes.
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This text covers material of a basic probability course, discrete stochastic processes including Martingale theory, continuous time stochastic processes like Brownian motion and stochastic differential equations, estimation theory, and more.
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This material was made available for the course Probability of the Mathematical Tripos. Contents: Basic Concepts; Axiomatic Probability; Discrete Random Variables; Continuous Random Variables; Inequalities, Limit Theorems and Geometric Probability.