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On Branching Processes in Random Environments
The Annals of Mathematical Statistics, 1969 $\{\zeta_n\}$ is a sequence of $\operatorname{iid}$ "environmental" variables in an abstract space $\Theta$. Each point $\zeta \varepsilon \Theta$ is associated with a $\operatorname{pgf} \phi_\zeta(s)$. The branching process $\{Z_n\}$ is defined as a Markov chain such that $Z_0 = k$, a finite integer, and given $Z_n$ and $\zeta_n, Z_{n+1}$ is ...
Smith, Walter L., Wilkinson, William E.
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φ-branching processes in a random environment [PDF]
Applicationes Mathematicae, 1984 Let \(\phi\) be a function mapping the set of non-negative integers into itself such that \(\phi (0)=0\). Consider a sequence of integer valued random variables \(\{Z_ n\), \(n=0,1,...\}\) and suppose that they satisfy the condition \[ Z_ 0=m,\quad E(s^{Z_{n+1}}| {\mathcal F}_ n({\bar\xi }))=[f_{\xi_ n}(s)]^{\phi (Z_ n)},\quad n\geq 0,| s|\leq 1 ...
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mSystems, 2021 In recent years, our appreciation of the extent of habitable environments in Earth’s subsurface has greatly expanded, as has our understanding of the biodiversity contained within.
Lindsay I. Putman +7 more
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Occupation time theorems for one-dimensional random walks and diffusion processes in random environments [PDF]
, 2008 journal ...
KASAHARA Yuji, Watanabe Shinzo
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Tail asymptotics for cumulative processes sampled at heavy-tailed random times with applications to queueing models in Markovian environments [PDF]
, 2013 This paper considers the tail asymptotics for a cumulative process $\{B(t); t \ge 0\}$ sampled at a heavy-tailed random time $T$. The main contribution of this paper is to establish several sufficient conditions for the asymptotic equality ${\sf P}(B(T) >
Masuyama, Hiroyuki
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Frequency-specific modulation of population-level frequency tuning in human auditory cortex
BMC Neuroscience, 2009 Background Under natural circumstances, attention plays an important role in extracting relevant auditory signals from simultaneously present, irrelevant noises.
Roberts Larry E +4 more
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Perturbing transient random walk in a random environment with cookies of maximal strength [PDF]
, 2013 . We consider a left-transient random walk in a random environment on Z that will be disturbed by cookies inducing a drift to the right of strength 1. The number of cookies per site is i.i.d. and independent of the environment.
Bauernschubert, Elisabeth
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The Contact Processes in a Random Environment
The Annals of Probability, 1991 This paper deals with one-dimensional contact process in an i.i.d. environment (CPRE). Let \(\xi_ t\subset\mathbb{Z}\) be the state of the process at time \(t\). Then, the dynamics are formulated as follows: a) Particles are born at unoccupied sites \(x\) at rate \(|\xi_ t\cap\{x- 1, x+1\}|\).
Bramson, Maury +2 more
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Birth and death processes in interactive random environments
Queueing Systems, 2022 This paper studies birth and death processes in interactive random environments where the birth and death rates and the dynamics of the state of the environment are dependent on each other. Two models of a random environment are considered: a continuous-time Markov chain (finite or countably infinite) and a reflected (jump) diffusion process.
Guodong Pang +2 more
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Band Codes for Energy-Efficient Network Coding with Application to P2P Mobile Streaming [PDF]
, 2013 A key problem in random network coding (NC) lies in the complexity and energy consumption associated with the packet decoding processes, which hinder its application in mobile environments.
Bioglio, Valerio +4 more
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