Abstract
This note presents four sets of problems. The first suggests the possibility of a limit theory for null-recurrent renewal processes similar to the theory in the positive recurrent case. The second concerns exact coupling of random walks on the line with step-lengths that are neither discrete nor spread out. The third concerns the coupling characterization of setwise convergence of distributions of stochastic processes to a stationary limit. The fourth concerns characterizations of mass-stationarity, a concept formalizing the intuitive idea that the origin is a typical location in the mass of a random measure. Mass-stationarity is an intrinsic characterization of Palm versions with respect to stationary random measures.
Similar content being viewed by others
References
Arnaldsson, O.: On Coupling of Discrete Random Walks on the Line. Master Thesis, Department of Mathematics, University of Iceland, (2010)
Heveling, M., Last, G.: Characterization of Palm measures via bijective point-shifts. Ann. Probab. 33, 1698–1715 (2005)
Heveling, M., Last, G.: Point shift characterization of Palm measures on Abelian groups. Electron. J. Probab. 12, 122–137 (2007)
Last, G.: Modern random measures: Palm theory and related models. In: Kendall, W., Molchanov, I. (eds.) New Perspectives in Stochastic Geometry. Oxford University Press, Oxford (2010)
Last, G., Thorisson, H.: Invariant transports of stationary random measures and mass-stationarity. Ann. Probab. 37, 790–813 (2009)
Last, G., Thorisson, H.: What is typical? J. Appl. Probab. 48A (2011)
Last, G., Thorisson, H.: Construction of stationary and mass-stationary random measures in ℝd (2011, in preparation)
Thorisson, H.: Coupling, Stationarity, and Regeneration. Springer, New York (2000)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Thorisson, H. Open problems in renewal, coupling and Palm theory. Queueing Syst 68, 313–319 (2011). https://doi.org/10.1007/s11134-011-9241-2
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11134-011-9241-2