Outputs (55)

Passage-times for partially-homogeneous reflected random walks on the quadrant (2025)
Journal Article
da Costa, C., Menshikov, M. V., & Wade, A. R. (2025). Passage-times for partially-homogeneous reflected random walks on the quadrant. Electronic Journal of Probability, 30, 1-34. https://doi.org/10.1214/25-EJP1313

We consider a random walk on the first quadrant of the square lattice, whose increment law is, roughly speaking, homogeneous along a finite number of half-lines near each of the two boundaries, and hence essentially specified by finitely-many transit... Read More about Passage-times for partially-homogeneous reflected random walks on the quadrant.

Brownian motion with asymptotically normal reflection in unbounded domains: from transience to stability (2025)
Journal Article
Brešar, M., Mijatović, A., & Wade, A. (2025). Brownian motion with asymptotically normal reflection in unbounded domains: from transience to stability. Annals of Probability, 53(1), 175-222. https://doi.org/10.1214/24-AOP1703

We quantify the asymptotic behaviour of multidimensional drifltess diffusions in domains unbounded in a single direction with asymptotically normal reflections from the boundary. We identify the critical growth/contraction rates of the domain that se... Read More about Brownian motion with asymptotically normal reflection in unbounded domains: from transience to stability.

Semi-infinite particle systems with exclusion interaction and heterogeneous jump rates (2025)
Journal Article
Menshikov, M. V., Popov, S., & Wade, A. R. (online). Semi-infinite particle systems with exclusion interaction and heterogeneous jump rates. Mathematical Sciences, https://doi.org/10.1007/s00440-024-01357-2

We study semi-infinite 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 suppre... Read More about Semi-infinite particle systems with exclusion interaction and heterogeneous jump rates.

Iterated-logarithm laws for convex hulls of random walks with drift (2024)
Journal Article
Cygan, W., Sandrić, N., Šebek, S., & Wade, A. R. (2024). Iterated-logarithm laws for convex hulls of random walks with drift. Transactions of the American Mathematical Society, 377(9), 6695-6724

We establish laws of the iterated logarithm for intrinsic volumes of the convex hull of many-step, multidimensional random walks whose increments have two moments and a non-zero drift. Analogous results in the case of zero drift, where the scaling is... Read More about Iterated-logarithm laws for convex hulls of random walks with drift.

Superdiffusive planar random walks with polynomial space–time drifts (2024)
Journal Article
da Costa, C., Menshikov, M., Shcherbakov, V., & Wade, A. (2024). Superdiffusive planar random walks with polynomial space–time drifts. Stochastic Processes and their Applications, 176, Article 104420. https://doi.org/10.1016/j.spa.2024.104420

We quantify superdiffusive transience for a two-dimensional random walk in which the vertical coordinate is a martingale and the horizontal coordinate has a positive drift that is a polynomial function of the individual coordinates... Read More about Superdiffusive planar random walks with polynomial space–time drifts.

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. (2023). 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. (2024). Strong transience for one-dimensional Markov chains with asymptotically zero drifts. Stochastic Processes and their Applications, 170, Article 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 / x as x → ∞ , we quantify degree of transience via existence of moments for conditional retu... Read More about Strong transience for one-dimensional Markov chains with asymptotically zero drifts.

Energy-Constrained Random Walk with Boundary Replenishment (2023)
Journal Article
Wade, A. R., & Grinfeld, M. (2023). Energy-Constrained Random Walk with Boundary Replenishment. Journal of Statistical Physics, 190(10), Article 155. https://doi.org/10.1007/s10955-023-03165-9

We study an energy-constrained random walker on a length-N interval of the one-dimensional integer lattice, with boundary reflection. The walker consumes one unit of energy for every step taken in the interior, and energy is replenished up to a capac... Read More about Energy-Constrained Random Walk with Boundary Replenishment.