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Path probability of stochastic motion: A functional approach

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  • Masayuki Hattori
  • Sumiyoshi Abe

Abstract

The path probability of a particle undergoing stochastic motion is studied by the use of functional technique, and the general formula is derived for the path probability distribution functional. The probability of finding paths inside a tube/band, the center of which is stipulated by a given path, is analytically evaluated in a way analogous to continuous measurements in quantum mechanics. Then, the formalism developed here is applied to the stochastic dynamics of stock price in finance.

Suggested Citation

  • Masayuki Hattori & Sumiyoshi Abe, 2016. "Path probability of stochastic motion: A functional approach," Papers 1602.04363, arXiv.org.
    • Handle: RePEc:arx:papers:1602.04363
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    File URL: http://arxiv.org/pdf/1602.04363
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