All Outputs (3)

Non-Homogeneous Random Walks: Lyapunov Function Methods for Near-Critical Stochastic Systems (2016)
Book
Menshikov, M., Popov, S., & Wade, A. (2016). Non-Homogeneous Random Walks: Lyapunov Function Methods for Near-Critical Stochastic Systems. Cambridge University Press. https://doi.org/10.1017/9781139208468

Anomalous recurrence properties of many-dimensional zero-drift random walks (2016)
Journal Article
Georgiou, N., Menshikov, M. V., Mijatovic, A., & Wade, A. R. (2016). Anomalous recurrence properties of many-dimensional zero-drift random walks. Advances in Applied Probability, 48(Issue A), 99-118. https://doi.org/10.1017/apr.2016.44

Famously, a d-dimensional, spatially homogeneous random walk whose increments are nondegenerate, have finite second moments, and have zero mean is recurrent if d∈{1,2}, but transient if d≥3. Once spatial homogeneity is relaxed, this is no longer true... Read More about Anomalous recurrence properties of many-dimensional zero-drift random walks.

Random dynamical systems with systematic drift competing with heavy-tailed randomness (2016)
Journal Article
Belitsky, V., Menshikov, M., Petritis, D., & Vachkovskaia, M. (2016). Random dynamical systems with systematic drift competing with heavy-tailed randomness. Markov processes and related fields, 22(4), 629-652

Motivated by the study of the time evolution of random dynamical systems arising in a vast variety of domains --- ranging from physics to ecology --- we establish conditions for the occurrence of a non-trivial asymptotic behaviour for these systems i... Read More about Random dynamical systems with systematic drift competing with heavy-tailed randomness.