Mathematics - Probability62L20An algorithm of searching a zero of an unknown undimensional function is considered, measured at a point x with some error. The step sizes are random positive values and are calculated according to the rule: if two consecutive iterations are in same direction step ...
The steady-state properties of the bistable kinetic model are analyzed. We find the following. (1) In the alpha-D parameter plane (alpha and D are the additive noise and multiplicative noise intensities, respectively), the area of the bimodal region of the stationary probability distribution (...
E{x} stands for the mathematical expectation of x. ≔N≔{0,1,2,⋯}. diag{⋯} is a block-diagonal matrix. (Ω,F,{Fk}k∈N,Prob) is a filtered probability space where {Fk}k∈N is the family of sub σ-algebras of F generated by {wk}k∈N. Denote l2([0,∞),Rl) as ...
This paper investigates the design and analysis problem of H∞ filter for a class of nonlinear systems based on T-S fuzzy models with both multiplicative noises and redundant channels, which are governed by a set of Bernoulli distributed white sequences. The packet dropout’s probability of the...
However, we might want a stronger assurance of the performance of MW; for example, we would like to know that the actual per-iteration loss is, with high probability, close to the expected value. As the following lemma shows, the per-trial loss of any algorithm for the repeated game is...
weightmethodsofLittlestoneandWarmuth,isanalyzedusingtheKullback-Liebler divergence.Thisanalysisyieldsanew,simpleproofoftheminmaxtheorem,aswellasaprovablemethod ofapproximatelysolvingagame.Avariantofourgame-playingalgorithmisprovedtobeoptimalina verystrongsense. 1Introduction Westudytheproblemoflearningtoplayarepeated...
In particular, we focus on density estimation problems and the aim is to define a suitable estimator, using a multiplicative combination of elementary density functions, which correspond to simplified or partially specified probability models for the interest random phenomenon. The boosting algorithm ...
Wang. The augmented multiplicative coaslescent, bounded size rules and critical dynamics of random graphs. Probability Theory and Related Fields, 2013. To appear.S. Bhamidi, A. Budhiraja, and X. Wang. The augmented multiplicative coalescent, bounded size rules and critical dynamics of random ...
Assuming a Gaussian probability density function of the response process and by choosing the weighting functions in a suitable way, the equivalence of the proposed method, called "Gaussian Probabilistic Linearization" (GPL), with the "Gaussian Stochastic Linearization" (GSL) applied to the coefficients...
Mathematics - Probability60C0505C8090B15Random graph models with limited choice have been studied extensively with the goal of understanding the mechanism of the emergence of the giant component. One of the standard models are the Achlioptas random graph processes on a fixed set of $n$ vertices...