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Complex-valued Wiener measure: An approach via random walk in the complex plane

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  • Jumarie, Guy

Abstract

In the present paper, it is shown that the heat equation of order n and its companion complex-valued Brownian motion of order n can be obtained in a very simple manner as the limit of a random walk defined in the complex plane, by means of the complex roots of the unity. This probabilistic model unifies Hochberg's and Sainty's approaches, and its main advantages is to enlighten the practical physical meaning of signed measures of probability (Hochberg), and to suggest simulation techniques. The complex-valued Brownian motion of order 4 should be of direct application in computer vision, as a result of the definition of image in terms of pixel.

Suggested Citation

  • Jumarie, Guy, 1999. "Complex-valued Wiener measure: An approach via random walk in the complex plane," Statistics & Probability Letters, Elsevier, vol. 42(1), pages 61-67, March.
    • Handle: RePEc:eee:stapro:v:42:y:1999:i:1:p:61-67
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    Cited by:

    1. Beghin, L. & Orsingher, E. & Ragozina, T., 2001. "Joint distributions of the maximum and the process for higher-order diffusions," Stochastic Processes and their Applications, Elsevier, vol. 94(1), pages 71-93, July.

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