Results 51 to 60 of about 23,064 (196)
Some Generalized Entropy Ergodic Theorems for Nonhomogeneous Hidden Markov Models
MathematicsEntropy measures the randomness or uncertainty of a stochastic process, and the entropy rate refers to the limit of the time average of entropy.
Qifeng Yao +3 more
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Illinois Journal of Mathematics, 2000 Let \(\{T_t\}_{t\in\mathbb{R}}\) be a measure preserving flow on a probability space \((X,\beta, m)\). Let \((\varepsilon_k)\) be a sequence in \((0,1)\), and let \(\phi\) be a positive integrable function on \(\mathbb{R}\) satisfying (i) \(\int\phi(x) dx= 1\), and (ii) the function \(\Phi(x)= \sup_{|y|\geq|x|}\phi(y)\) is integrable.
openaire +3 more sources
Wave Tracing: Generalizing The Path Integral To Wave Optics
Computer Graphics Forum, EarlyView.Abstract Modeling the wave nature of light and the propagation and diffraction of electromagnetic fields is crucial for the accurate simulation of many phenomena, yet wave simulations are significantly more computationally complex than classical ray‐based models.
Shlomi Steinberg, Matt Pharr
wiley +1 more source
Deviation of ergodic averages for rational polygonal billiards
, 2007 We prove polynomial upper bounds for the deviation of ergodic averages for the straight line flow on every translation surface in almost every direction, in particular for those surfaces arising from rational polygonal billiards.Comment: to appear in ...
Athreya, Jayadev S., Forni, Giovanni
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A Comparative Review of Specification Tests for Diffusion Models
International Statistical Review, EarlyView.Summary Diffusion models play an essential role in modelling continuous‐time stochastic processes in the financial field. Therefore, several proposals have been developed in the last decades to test the specification of stochastic differential equations.
A. López‐Pérez +3 more
wiley +1 more source
Noncommutative Multi-Parameter Subsequential Wiener–Wintner-Type Ergodic Theorem
AxiomsThis paper is devoted to the study of a multi-parameter subsequential version of the “Wiener–Wintner” ergodic theorem for the noncommutative Dunford–Schwartz system.
Mu Sun, Yinmei Zhang
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Convergence of weighted ergodic averages
, 2020 Let $(X, \mathcal{A}, )$ be a probability space and let $T$ be a contraction on $L^2( )$. We provide suitable conditions over sequences $(w_k)$, $(u_k)$ and $(A_k)$ in such a way that the weighted ergodic limit $\lim\limits_{N\rightarrow\infty}\frac{1}{A_N}\sum_{k=0}^{N-1} w_k T^{u_k}(f)=0$ $ $-a.e. for any function $f$ in $L^2( )$.
Darwiche, Ahmad, Schneider, Dominique
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On Integral Priors for Multiple Comparison in Bayesian Model Selection
International Statistical Review, EarlyView.Summary Noninformative priors constructed for estimation purposes are usually not appropriate for model selection and testing. The methodology of integral priors was developed to get prior distributions for Bayesian model selection when comparing two models, modifying initial improper reference priors. We propose a generalisation of this methodology to
Diego Salmerón +2 more
wiley +1 more source
Ergodicity of the Liouville system implies the Chowla conjecture
Discrete Analysis, 2017 Ergodicity of the Liouville system implies the Chowla conjecture, Discrete Analysis 2017:19, 41 pp. The Liouville function $\lambda:\mathbb N\to\{-1,1\}$ takes a product $p_1p_2\dots p_k$ of (not necessarily distinct) primes $p_1,\dots,p_k$ to $(-1)^k$.
Nikos Frantzikinakis
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ERGODIC AVERAGES FOR INDEPENDENT POLYNOMIALS AND APPLICATIONS [PDF]
Journal of the London Mathematical Society, 2006 12 ...
Frantzikinakis, Nikos, Kra, Bryna
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