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Transactions of the Karelian Research Centre of the Russian Academy of Sciences, 2015 The problem of optimal control in a random environment (also known as the two- armed bandit problem) is considered. The equations for calculating Bayes risks and losses are obtained for incomes with different variances.
Aleksey Lazutchenko
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Random Walks in Cooling Random Environments [PDF]
, 2019 We propose a model of a one-dimensional random walk in dynamic random environment that interpolates between two classical settings: (I) the random environment is sampled at time zero only; (II) the random environment is resampled at every unit of time. In our model the random environment is resampled along an increasing sequence of deterministic times.
Avena L, den Hollander F
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Deterministic walks in random environment [PDF]
, 2020 Motivated by the random Lorentz gas, we study deterministic walks in random environment and show that (in simple, yet relevant cases) they can be reduced to a class of random walks in random environment where the jump probability depends (weakly) on the ...
Liverani, C, Aimino, R
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Random Walks in Random Environments [PDF]
, 2006 Random walks provide a simple conventional model to describe various transport processes, for example propagation of heat or diffusion of matter through a medium. However, in many practical cases the medium is highly irregular due to defects, impurities, fluctuations etc., and it is natural to model this as random environment.
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Trees with product-form random weights [PDF]
Discrete Mathematics & Theoretical Computer Science, 2006 We consider growing random recursive trees in random environment, in which at each step a new vertex is attached according to a probability distribution that assigns the tree vertices masses proportional to their random weights.The main aim of the paper ...
Konstantin Borovkov, Vladimir Vatutin
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Random walk with barycentric self-interaction [PDF]
, 2010 We study the asymptotic behaviour of a $d$-dimensional self-interacting random walk $X_n$ ($n = 1,2,...$) which is repelled or attracted by the centre of mass $G_n = n^{-1} \sum_{i=1}^n X_i$ of its previous trajectory. The walk's trajectory $(X_1,...,X_n)
Volkov, S. +13 more
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Branching processes in random environment die slowly [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 Let $Z_n,n=0,1,\ldots,$ be a branching process evolving in the random environment generated by a sequence of iid generating functions $f_0(s),f_1(s),\ldots,$ and let $S_0=0$, $S_k=X_1+ \ldots +X_k,k \geq 1$, be the associated random walk with $X_i=\log ...
Vladimir Vatutin, Andreas Kyprianou
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Non-homogeneous random walks with non-integrable increments and heavy-tailed random walks on strips [PDF]
, 2012 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.
MacPhee, Iain M. +9 more
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Random environment on coloured trees [PDF]
, 2007 International audienceIn this paper we study a regular rooted coloured tree with random labels assigned to its edges, where the distribution of the label assigned to an edge depends on the colours of its endpoints.
Petritis, Dimitri +2 more
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Random walk on random walks [PDF]
, 2015 In this paper we study a random walk in a one-dimensional dynamic random environment consisting of a collection of independent particles performing simple symmetric random walks in a Poisson equilibrium with density ρ∈(0,∞)ρ∈(0,∞).
Hilário, Marcelo R. +4 more
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