Stochastic path integrals can be derived like quantum mechanical path integrals
Abstrak
Stochastic mechanics---the study of classical stochastic systems governed by things like master equations and Fokker-Planck equations---exhibits striking mathematical parallels to quantum mechanics. In this article, we make those parallels more transparent by presenting a quantum mechanics-like formalism for deriving a path integral description of systems described by stochastic differential equations. Our formalism expediently recovers the usual path integrals (the Martin-Siggia-Rose-Janssen-De Dominicis and Onsager-Machlup forms) and is flexible enough to account for different variable domains (e.g. real line versus compact interval), stochastic interpretations, arbitrary numbers of variables, explicit time-dependence, dimensionful control parameters, and more. We discuss the implications of our formalism for stochastic biology.
Topik & Kata Kunci
Penulis (2)
John J. Vastola
William R. Holmes
Akses Cepat
- Tahun Terbit
- 2019
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓