# Stochastic Bäcklund Transformations

Chapter

## Abstract

How does one introduce randomness into a classical dynamical system in order to produce something which is related to the ‘corresponding’ quantum system? We consider this question from a probabilistic point of view, in the context of some integrable Hamiltonian systems.

## Keywords

Stochastic Differential Equation Infinitesimal Generator Toda Lattice Martingale Problem Toda Chain
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Notes

### Acknowledgements

Thanks to Simon Ruijsenaars for valuable discussions and comments on an earlier draft, and Mark Adler and Tom Kurtz for helpful correspondence. Thanks also to the anonymous referee for helpful comments and suggestions.

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