We consider cyclic Lotka-Volterra models with three and four strategies where at every interaction agents play a strategy using a time-dependent probability distribution. Agents learn from a loss by reducing the probability to play a losing strategy at the next interaction. For that, an agent is described as an urn containing β balls of three and four types, respectively, where after a loss one...

We consider the problem of constructing robust nonparametric confidence intervals and tests of hypothesis for the median when the data distribution is unknown and the data may contain a small fraction of contamination. We propose a modification of the sign test (and its associated confidence interval) which attains the nominal significance level (probability coverage) for any distribution in th...

In this paper, we show a unified approach to the problem of characterizing general distribution functions based on the conditional expectation between adjacent order statistics, ξ(x) = E(h(Xr,n) | Xr+1,n = x) or ξ(x) = E(h(Xr+1,n) | Xr,n = x), where h is a real, continuous and strictly monotonic function. We have the explicit expression of the distribution function F from the above order mean f...

In the present paper, solvability of stochastic Helmholtz problem is investigated in class differential equations equivalent distribution. Earlier, by additional variables method was almost surely (a.s.). The study distribution allows us to significantly expand region its solvability. This due possibility using well-known methods theory processes, such as phase space transformation, absolutely ...

An equivalence between the Gurov-Reshetnyak GR(ε) and Muckenhoupt A∞ conditions is established. Our proof is extremely simple and works for arbitrary absolutely continuous measures. Throughout the paper, μ will be a positive measure on R absolutely continuous with respect to Lebesgue measure. Denote Ωμ(f ;Q) = 1 μ(Q) ∫ Q |f(x) − fQ,μ|dμ(x), fQ,μ = 1 μ(Q) ∫

We show that the integrated density of states of the almost Mathieu operator is absolutely continuous if and only if the coupling is non-critical. We deduce for subcritical coupling that the spectrum is purely absolutely continuous for almost every phase, settling the measure-theoretical case of Problem 6 of Barry Simon’s list of Schrödinger operator problems for the twenty-first century.