Time substitutions in stochastic processes as a tool in path integration. (English) Zbl 0619.60076
In this note, written for physicists, the authors review the technique of time changes of diffusion processes in order to apply it to the solution of Schrödinger equations of a particle in a potential.
The combined effect of coordinate changes and time changes on the solutions to diffusion equations is obtained via the representation of solutions as path integrals by means of the Feynman-Kac formula.
The combined effect of coordinate changes and time changes on the solutions to diffusion equations is obtained via the representation of solutions as path integrals by means of the Feynman-Kac formula.
Reviewer: H.Gzyl
MSC:
| 60J70 | Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
Keywords:
technique of time changes; solution of Schrödinger equations; representation of solutions as path integrals; Feynman-Kac formulaReferences:
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