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- Publisher
- Springer Journals
- Copyright
- Copyright
- Subject
- Mathematics; Computational Mathematics and Numerical Analysis; Applications of Mathematics; Partial Differential Equations; Probability Theory and Stochastic Processes; Calculus of Variations and Optimal Control; Optimization
- ISSN
- 0167-8019
- eISSN
- 1572-9036
- DOI
- 10.1007/BF00994913
- Publisher site
- See Article on Publisher Site
Abstract
We consider a stochastic bilinear system model for laser propagation in atmospheric turbulence. The model consists of a random Schrödinger equation in which the white noise input is multiplied by the state. We consider approximate product form solutions of the Trotter-Kato type, and use these product forms to relate the Hilbert space-valued white noise model and the Itô equation model. We also consider white noise as the limit of a sequence Ornstein-Uhlenbeck processes. Finally, we consider approximate solutions using the Feynman-Itô equation, and an approximate calculation of the mean field without using the Markov approximation.
Journal
Acta Applicandae Mathematicae – Springer Journals
Published: Dec 31, 2004