28 citations · 84 across the 33 of their papers we have counts for
40 papers
On extremes of a random walk with positive drift over an intermediate regularly varying time interval
Sergey Foss, Dmitry Korshunov
We consider a random walk with a finite positive drift that is stopped at a random time having an intermediate regularly varying distribution. We assume that the jump…
Maxima over random time intervals for heavy-tailed compound renewal and Lévy processes
Sergey Foss, Dmitry Korshunov, Zbigniew Palmowski
We derive subexponential tail asymptotics for the distribution of the maximum of a compound renewal process with linear component and of a Lévy process, both with negative drift, o…
Estimation of the last passage percolation constant in a charged complete directed acyclic graph via perfect simulation
Sergey Foss, Takis Konstantopoulos, Bastien Mallein +1
Our object of study is the asymptotic growth of heaviest paths in a charged (weighted with signed weights) complete directed acyclic graph. Edge charges are i.i.d. random variables…
Moments of the first descending epoch for a random walk with negative drift
Sergey Foss, Timofej Prasolov
We consider the first exit time from the positive halfline of a random walk with i.d.d. summands having a negative drif…
Non-standard limits for a family of autoregressive stochastic sequences
Sergey Foss, Matthias Schulte
We consider a family of multivariate autoregressive stochastic sequences that restart when hit a neighbourhood of the origin, and study their distributional limits when the autoreg…
Limit theorems for the maximal path weight in a directed graph on the line with random weights of edges
S. Foss, T. Konstantopoulos, A. Logachev +1
We consider the infinite directed graph with vertices the set of integers ...,-2,-1,0,1,2,... . Let v be a random variable taking either finite values or value "minus infinity". Co…
Structural Properties of Conditioned Random Walks on Integer Lattices with Random Local Constraints
Sergey Foss, Alexander Sakhanenko
We consider a random walk on a multidimensional integer lattice with random bounds on local times, conditioned on the event that it hits a high level before its death. We introduce…
Probabilistic and analytical properties of the last passage percolation constant in a weighted random directed graph
Sergey Foss, Takis Konstantopoulos, Artem Pyatkin
To each edge (i,j), i<j of the complete directed graph on the integers we assign unit weight with probability p or weight x with probability 1-p, independently from edge to edge, a…
Many greedy cleaners in a Poisson environment
Sergey Foss, Thomas Mountford
We introduce a new ``greedy cleaning'' model where a star-like state space (containing N half-lines connected by the origin) is covered by a homogeneous Poisson process of ``dust p…
Limiting properties of random graph models with vertex and edge weights
Sergey Foss, Takis Konstantopoulos
This paper provides an overview of results, concerning longest or heaviest paths, in the area of random directed graphs on the integers along with some extensions. We study first-o…
Tails in a fixed-point problem for a branching process with state-independent immigration
Sergey Foss, Masakiyo Miyazawa
We consider a fixed-point equation for a non-negative integer-valued random variable, that appears in branching processes with state-independent immigration. A similar equation app…
Limit theorems and structural properties of the Cat-and-Mouse Markov chain
Timofei Prasolov, Sergey Foss, Seva Shneer
We revisit the so-called Cat-and-Mouse Markov chain, studied earlier by Litvak and Robert (2012). This is a 2-dimensional Markov chain on the lattice , where the firs…
Customer sojourn time in GI/G/1 feedback queue in the presence of heavy tails
Sergey Foss, Masakiyo Miyazawa
We consider a single-server GI/GI/1 queueing system with feedback. We assume the service times distribution to be (intermediate) regularly varying. We find the tail asymptotics for…
Interference Queueing Networks on Grids
Abishek Sankararaman, François Baccelli, Sergey Foss
Consider a countably infinite collection of interacting queues, with a queue located at each point of the -dimensional integer grid, having independent Poisson arrivals, but dep…
Regular Variation in a Fixed-Point Problem for Single- and Multiclass Branching Processes and Queues
Søren Asmussen, Sergey Foss
Tail asymptotics of the solution to a fixpoint problem of type is derived under heavy-tailed conditions allowing both dependence between and …
Spatial random multiple access with multiple departure
Sergey Foss, Andrey Turlikov, Maxim Grankin
We introduce a new model of spatial random multiple access systems with a non-standard departure policy: all arriving messages are distributed uniformly on a finite sphere in the s…
Large-scale Join-Idle-Queue system with general service times
Sergey Foss, Alexander Stolyar
A parallel server system with identical servers is considered. The service time distribution has a finite mean , but otherwise is arbitrary. Arriving customers are be rout…
Stability and instability of a random multiple access model with adaptive energy harvesting
Sergey Foss, Dmitriy Kim, Andrey Turlikov
We introduce a model for the classical synchronised multiple access system with a single transmission channel and a randomised transmission protocol (ALOHA). We assume in addition…
Local stability in a transient Markov chain
Ivo Adan, Sergey Foss, Seva Shneer +1
We prove two propositions with conditions that a system, which is described by a transient Markov chain, will display local stability. Examples of such systems include partly overl…
Convolution and convolution-root properties of long-tailed distributions
Hui Xu, Sergey Foss, Yuebao Wang
We obtain a number of new general properties, related to the closedness of the class of long-tailed distributions under convolutions, that are of interest themselves and may be app…
Power law condition for stability of Poisson hail
Sergey Foss, Takis Konstantopoulos, Thomas Mountford
We consider the Poisson hail model introduced by Baccelli and Foss. We give a power law condition for the tails (spatial and temporal) of the distribution of jobs to ensure stabili…
Shape Theorems for Poisson Hail on a Bivariate Ground
François Baccelli, Héctor A. Chang-Lara, Sergey Foss
We consider the extension of the Euclidean stochastic geometry Poisson Hail model to the case where the service speed is zero in some subset of the Euclidean space and infinity in…
Two-node queueing network with a heavy-tailed random input: the strong stability case
Sergey Foss, Masakiyo Miyazawa
We consider a two-node fluid network with batch arrivals of random size having a heavy-tailed distribution. We are interested in the tail asymptotics for the stationary distributio…
Stability of a Random Multiple Access Channel with "Success-Failure" Feedback
Sergey Foss, Bruce Hajek, Andrey Turlikov
We consider a model of a decentralized multiple access system with a non-standard binary feedback where the empty and collision situations cannot be distinguished. We show that, li…