Path probability of stochastic motion: A functional approach
  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. 
Masayuki Hattori, Sumiyoshi Abe
cond-mat.stat-mech q-fin.GN quant-ph