Outputs (55)

On the centre of mass of a random walk (2018)
Journal Article
Lo, C. H., & Wade, A. R. (2019). On the centre of mass of a random walk. Stochastic Processes and their Applications, 129(11), 4663-4686. https://doi.org/10.1016/j.spa.2018.12.007

For a random walk Sn on Rd we study the asymptotic behaviour of the associated centre of mass process Gn=n−1∑ni=1Si. For lattice distributions we give conditions for a local limit theorem to hold. We prove that if the increments of the walk have zero... Read More about On the centre of mass of a random walk.

A radial invariance principle for non-homogeneous random walks (2018)
Journal Article
Georgiou, N., Mijatović, A., & Wade, A. R. (2018). A radial invariance principle for non-homogeneous random walks. Electronic Communications in Probability, 23, Article 56. https://doi.org/10.1214/18-ecp159

Consider non-homogeneous zero-drift random walks in Rd, d≥2, with the asymptotic increment covariance matrix σ2(u) satisfying u⊤σ2(u)u=U and trσ2(u)=V in all in directions u∈Sd−1 for some positive constants U<V. In this paper we establish weak conver...

Heavy-tailed random walks on complexes of half-lines (2017)
Journal Article
Menshikov, M. V., Petritis, D., & Wade, A. R. (2018). Heavy-tailed random walks on complexes of half-lines. Journal of Theoretical Probability, 31(3), 1819-1859. https://doi.org/10.1007/s10959-017-0753-5

We study a random walk on a complex of finitely many half-lines joined at a common origin; jumps are heavy-tailed and of two types, either one-sided (towards the origin) or two-sided (symmetric). Transmission between half-lines via the origin is gove... Read More about Heavy-tailed random walks on complexes of half-lines.

Non-homogeneous random walks on a half strip with generalized Lamperti drifts (2017)
Journal Article
Lo, C. H., & Wade, A. R. (2017). Non-homogeneous random walks on a half strip with generalized Lamperti drifts. Markov processes and related fields, 23(1), 125-146

We study a Markov chain on Undefined control sequence \RP, where Undefined control sequence \RP is the non-negative real numbers and S is a finite set, in which when the Undefined control sequence \RP-coordinate is large, the S-coordinate of the proc... Read More about Non-homogeneous random walks on a half strip with generalized Lamperti drifts.

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.

Convex hulls of random walks and their scaling limits (2015)
Journal Article
Wade, A. R., & Xu, C. (2015). Convex hulls of random walks and their scaling limits. Stochastic Processes and their Applications, 125(11), 4300-4320. https://doi.org/10.1016/j.spa.2015.06.008

For the perimeter length and the area of the convex hull of the first n steps of a planar random walk, we study n→∞ mean and variance asymptotics and establish non-Gaussian distributional limits. Our results apply to random walks with drift (for the... Read More about Convex hulls of random walks and their scaling limits.

Phase transitions for random geometric preferential attachment graphs (2015)
Journal Article
Jordan, J., & Wade, A. R. (2015). Phase transitions for random geometric preferential attachment graphs. Advances in Applied Probability, 47(2), 565-588. https://doi.org/10.1239/aap/1435236988

Vertices arrive sequentially in space and are joined to existing vertices at random according to a preferential rule combining degree and spatial proximity. We investigate phase transitions in the resulting graph as the relative strengths of these tw... Read More about Phase transitions for random geometric preferential attachment graphs.

Random processes (2015)
Book Chapter
Cruise, R. J., Hryniv, O., & Wade, A. R. (2015). Random processes. In M. Grinfeld (Ed.), Mathematical Tools for Physicists (3-38). (2nd ed.). Wiley. https://doi.org/10.1002/3527600434.eap382.pub2

Convergence in a multidimensional randomized Keynesian beauty contest (2015)
Journal Article
Grinfeld, M., Volkov, S., & Wade, A. R. (2015). Convergence in a multidimensional randomized Keynesian beauty contest. Advances in Applied Probability, 47(1), 57-82. https://doi.org/10.1239/aap/1427814581

We study the asymptotics of a Markovian system of N ≥ 3 particles in [0, 1]d in which, at each step in discrete time, the particle farthest from the current centre of mass is removed and replaced by an independent U[0, 1]d random particle. We show th... Read More about Convergence in a multidimensional randomized Keynesian beauty contest.