| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 976576 | Physica A: Statistical Mechanics and its Applications | 2016 | 7 Pages |
•The concept of path probability of a random walker is studied.•The general formula for the path probability distribution functional is derived.•The overdamped limit of the formula is evaluated.•The probability of finding paths inside a given tube is calculated.•The theory developed here is applied to the problem of stock price in finance.
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.
