Path probability of stochastic motion: A functional approach
arXiv:1602.04363 · doi:10.1016/j.physa.2016.01.053
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.
arXiv comment19 pages, 2 figures
References in corpus (4)
- Aging and scaling of aftershocks
- Violation of the scaling relation and non-Markovian nature of earthquake aftershocks
- Aftershocks in Modern Perspectives: Complex Earthquake Network, Aging, and Non-Markovianity
- Path probability distribution of stochastic motion of non dissipative systems: a classical analog of Feynman factor of path integral