Random processes and random systems: An introduction-Reference-Cited by-同舟云学术

Random processes and random systems: An introduction

Published:1983 Issue: Volume: Page:1-108
ISSN:0075-8434
Container-title:Lecture Notes in Mathematics
language:
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Author:

Hughes Barry D.,Prager Stephen

Publisher

Springer Berlin Heidelberg

Link

http://link.springer.com/content/pdf/10.1007/BFb0073255

Reference223 articles.

1. K. Pearson, "The problem of the random walk", Nature 72 (1905) 294. In the less abstract half of the random walk literature it has become something of a tradition to commence articles with a direct quote of all or part of this letter, or at least to reproduce it in a footnote. Physicists may be amused to note that on the same page as Pearson's letter, J.H. Jeans argues at some length that Planck's constant h cannot possibly have a non-zero value!

2. Lord Rayleigh, "On the resultant of a large number of vibrations of the same pitch and of arbitrary phase", Phil. Mag. 10 (1880) 73–78, reprinted in Scientific Papers Vol 1, pp. 491–496 (Dover, New York, 1964). Rayleigh's derivation is elementary, but insightful: he analyses first vibrations with random phases 0 or π, then vibrations with phases 0, π/2, π, 3π/2, and then establishes that his conclusions hold more generally. Later ["On James Bernoulli's theorem in probabilities" Phil. Mag. 47 (1889) 246–251, reprinted in Scientific Papers Vol 4, pp. 370–375 (Dover, New York, 1964), and The Theory of Sound, Volume 1, 2nd edition, pp. 35–42 (New York, Dover, 1945)] he obtained the same results by approximating a difference equation describing the process by the diffusion equation.

3. Lord Rayleigh, "The problem of the random walk", Nature 72 (1905) 318, reprinted in Scientific Papers, Vol 5, p. 256.

4. K. Pearson, "The problem of the random walk", Nature 72 (1905) 342. Pearson concludes that: "the lesson of Lord Rayleigh's solution is that in open country the most probable place to find a drunken man who is at all capable of keeping on his feet is somewhere near his starting point!"

5. J.C. Kluyver, "A local probability problem", Proceedings of the Section of Sciences, Koninklijke Akademie van Wetenschappen te Amsterdam 8 (1906) 341–350 (Amsterdam, Johannes Müller, 1906: cover to cover translation of the original Dutch).

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