For the linearized Boltzmann equation with finite cross section, the solution is represented as an integral over the paths of a Markov jump process. The integral is only shown to converge conditionally, where the limiting process is defined by an increasing sequence of stopping times. The notion of local martingale plays an important role. A number of related kinetic models are also mentioned.
- Linearized Boltzmann equation
- jump Markov process
- multiplicative functional
- path integral representation
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics