Distributions of Functionals of Diffusions with Nonstandard Switching

摘要

The paper deals with the results that allow one to calculate the joint distributions of functionals of diffusions with switchings that occur at random time moments depending on the diffusion trajectory. Standard switchings from one set of diffusion coefficients to another occur at random time moments corresponding to the jump moments of a Poisson process independent of the initial diffusions. More general nonstandard switching occurs when the integral functional of the trajectory reaches the value equal to an exponentially distributed variable. With unit integrand such switching becomes standard.