Geodesic
Distributions of functionals of Brownian motion with non-standard switching
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 28, Tome 486 (2019), pp. 35-43

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The standard switching from one set of diffusion coefficients to another occurs at random times corresponding to the moments of jumps of Poisson process independent of the initial diffusion. The paper deals with the process of Brownian motion with variances taking one of two values by the switching, depending on a trajectories of the process. The most attractive from a computational point of view is the moment inverse to local time. 
@article{ZNSL_2019_486_a1,
     author = {A. N. Borodin},
     title = {Distributions of functionals of {Brownian} motion with non-standard switching},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {35--43},
     publisher = {mathdoc},
     volume = {486},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_486_a1/}
}
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A. N. Borodin. Distributions of functionals of Brownian motion with non-standard switching. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 28, Tome 486 (2019), pp. 35-43. http://geodesic.mathdoc.fr/item/ZNSL_2019_486_a1/