Outputs (4)

Dynamics of the non-homogeneous supermarket model (2012)
Journal Article
MacPhee, I., Menshikov, M., & Vachkovskaia, M. (2012). Dynamics of the non-homogeneous supermarket model. Stochastic Models, 28(4), 533-556. https://doi.org/10.1080/15326349.2012.726031

We consider the long term behavior of a Markov chain ξ(t) on ℤ N based on the N station supermarket model with general neighborhoods, arrival rates and service rates. Different routing policies for the model give different Markov chains. We show that... Read More about Dynamics of the non-homogeneous supermarket model.

On a general many-dimensional excited random walk (2012)
Journal Article
Menshikov, M., Popov, S., Ramírez, A. F., & Vachkovskaia, M. (2012). On a general many-dimensional excited random walk. Annals of Probability, 40(5), 2106-2130. https://doi.org/10.1214/11-aop678

In this paper we study a substantial generalization of the model of excited random walk introduced in [Electron. Commun. Probab. 8 (2003) 86–92] by Benjamini and Wilson. We consider a discrete-time stochastic process (Xn,n=0,1,2,…) taking values on Z... Read More about On a general many-dimensional excited random walk.

On range and local time of many-dimensional submartingales (2012)
Journal Article
Menshikov, M., & Popov, S. (2014). On range and local time of many-dimensional submartingales. Journal of Theoretical Probability, 27(2), 601-617. https://doi.org/10.1007/s10959-012-0431-6

We consider a discrete-time process adapted to some filtration which lives on a (typically countable) subset of ℝ d , d≥2. For this process, we assume that it has uniformly bounded jumps, and is uniformly elliptic (can advance by at least some fixed... Read More about On range and local time of many-dimensional submartingales.

Non-homogeneous random walks with non-integrable increments and heavy-tailed random walks on strips (2012)
Journal Article
Hryniv, O., MacPhee, I. M., Menshikov, M. V., & Wade, A. R. (2012). Non-homogeneous random walks with non-integrable increments and heavy-tailed random walks on strips. Electronic Journal of Probability, 17, Article 59. https://doi.org/10.1214/ejp.v17-2216

We study asymptotic properties of spatially non-homogeneous random walks with non-integrable increments, including transience, almost-sure bounds, and existence and non existence of moments for first-passage and last-exit times. In our proofs we also... Read More about Non-homogeneous random walks with non-integrable increments and heavy-tailed random walks on strips.