How to Apply Large Deviation Theory to Routing in WSNs

2014 ◽  
pp. 405-414
Author(s):  
János Levendovszky ◽  
Hoc Nguyen Thai
Keyword(s):  
Large Deviation ◽  
Large Deviation Theory ◽  
Deviation Theory

Large deviations in the supercritical branching process

1993 ◽  
Vol 25 (04) ◽  
pp. 757-772 ◽  
Author(s):  
J. D. Biggins ◽  
N. H. Bingham
Keyword(s):  
Distribution Function ◽  
Large Deviations ◽  
Population Size ◽  
Branching Process ◽  
Large Deviation ◽  
Moment Generating Function ◽  
Large Deviation Theory ◽  
Tail Behaviour ◽  
The Moment ◽  
Deviation Theory

The tail behaviour of the limit of the normalized population size in the simple supercritical branching process, W, is studied. Most of the results concern those cases when a tail of the distribution function of W decays exponentially quickly. In essence, knowledge of the behaviour of transforms can be combined with some ‘large-deviation' theory to get detailed information on the oscillation of the distribution function of W near zero or at infinity. In particular we show how an old result of Harris (1948) on the asymptotics of the moment-generating function of W translates to tail behaviour.

ON LOGARITHMIC ASYMPTOTICS OF STOCHASTIC RESONANCE FREQUENCIES

2003 ◽  
Vol 03 (01) ◽  
pp. 55-71
Author(s):  
S. C. CARMONA ◽  
M. I. FREIDLIN
Keyword(s):  
Dynamical Systems ◽  
Stochastic Resonance ◽  
Small Amplitude ◽  
Large Deviation ◽  
Large Deviation Theory ◽  
Resonance Effects ◽  
Resonance Frequencies ◽  
Logarithmic Asymptotics ◽  
The Relationship ◽  
Deviation Theory

Stochastic resonance effects due to arbitrarily small amplitude deterministic perturbations in dynamical systems with noise are studied. The concept of Log-Asymptotic Resonance Frequency is introduced and the relationship between its existence and some types of symmetries in the stochastic system is established; the spectrum of this kind of frequencies is determined. These symmetries are defined through the quasi-deterministic approximation of the system. The large deviation theory gives the basic machinery for this analysis.

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