Radically Elementary Probability Theory
by Edward Nelson
Publisher: Princeton University Press 1987
Number of pages: 111
Nelson develops a new approach to probability theory that is just as powerful as but much simpler than conventional Kolmogorov-style probability theory used throughout mathematics for most of the 20th century.
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by E. T. Jaynes - Cambridge University Press
The book is addressed to readers familiar with applied mathematics at the advanced undergraduate level. The text is concerned with probability theory and all of its mathematics, but now viewed in a wider context than that of the standard textbooks.
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Topics: Brownian Motion; Diffusion Processes; Weak convergence and Compactness; Stochastic Integrals and Ito's formula; Markov Processes, Kolmogorov's equations; Stochastic Differential Equations; Existence and Uniqueness; Girsanov Formula; etc.
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In 1999, Gian-Carlo Rota gave his famous course, Probability, at MIT for the last time. The late John N. Guidi taped the lectures and took notes which he then wrote up in a verbatim manner conveying the substance and the atmosphere of the course.
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History of the probability theory from the time of Pascal to that of Laplace (1865). Todhunter gave a close account of the difficulties involved and the solutions offered by each investigator. His studies were thorough and fully documented.