Outputs (4)

Stochastic billiards with Markovian reflections in generalized parabolic domains (2023)
Journal Article
da Costa, C., Menshikov, M. V., & Wade, A. R. (2023). Stochastic billiards with Markovian reflections in generalized parabolic domains. Annals of Applied Probability, 33(6B), 5459-5496. https://doi.org/10.1214/23-AAP1952

We study recurrence and transience for a particle that moves at constant velocity in the interior of an unbounded planar domain, with random reflections at the boundary governed by a Markov kernel producing outgoing angles from incoming angles. Our d... Read More about Stochastic billiards with Markovian reflections in generalized parabolic domains.

Reflecting Brownian motion in generalized parabolic domains: explosion and superdiffusivity (2023)
Journal Article
Menshikov, M. V., Mijatović, A., & Wade, A. R. (2023). Reflecting Brownian motion in generalized parabolic domains: explosion and superdiffusivity. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 59(4), 1813-1843. https://doi.org/10.1214/22-AIHP1309

For a multidimensional driftless diffusion in an unbounded, smooth, sub-linear generalized parabolic domain, with oblique reflection from the boundary, we give natural conditions under which either explosion occurs, if the domain narrows sufficiently... Read More about Reflecting Brownian motion in generalized parabolic domains: explosion and superdiffusivity.

Dynamics of Finite Inhomogeneous Particle Systems with Exclusion Interaction (2023)
Journal Article
Malyshev, V., Menshikov, M. V., Popov, S., & Wade, A. (in press). Dynamics of Finite Inhomogeneous Particle Systems with Exclusion Interaction. Journal of Statistical Physics, 190(11), Article 184. https://doi.org/10.1007/s10955-023-03190-8

We study finite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction which suppresses ju... Read More about Dynamics of Finite Inhomogeneous Particle Systems with Exclusion Interaction.

Strong transience for one-dimensional Markov chains with asymptotically zero drifts (2023)
Journal Article
Lo, C. H., Menshikov, M. V., & Wade, A. R. (2023). Strong transience for one-dimensional Markov chains with asymptotically zero drifts. Stochastic Processes and their Applications, 104260. https://doi.org/10.1016/j.spa.2023.104260

For near-critical, transient Markov chains on the non-negative integers in the Lamperti regime, where the mean drift at x decays as 1... Read More about Strong transience for one-dimensional Markov chains with asymptotically zero drifts.