We present the Lagrange multiplier rule, one of the basic optimization methods, in a new way. Novel features include: • Explanation of the true source of the power of the rule: reversal of tasks, but not the use of multipliers. • A natural proof based on a simple picture, but not the usual...

We present the Lagrange multiplier rule, one of the basic optimization methods, in a new way. Novel features include: • Explanation of the true source of the power of the rule: reversal of tasks, but not the use of multipliers. • A natural proof based on a simple picture, but not the...

The paper proposes an approach to evaluate hypotheses about transition dynamics when only the distributions at two points in time are observed. Using the principle of statistical mechanics, we show how to adjust in the most probable way a hypothesis so that it becomes compatible with the...

We study two tests for the equality of two population mean vectors under high dimensionality and column-wise dependence by thresholding. They are designed for better power performance when the mean vectors of two populations differ only in sparsely populated coordinates. The first test is...

Given a Brownian Motion W, in this paper we study the asymptotic behavior, as ε→0, of the quadratic covariation between f(εW) and W in the case in which f is not smooth. Among the main features discovered is that the speed of the decay in the case f∈Cα is at least polynomial in ε and not...

We compute a closed-form expression for the moment generating function fˆ(x;λ,α)=1λEx(eαLτ), where Lt is the local time at zero for standard Brownian motion with reflecting barriers at 0 and b, and τ∼Exp(λ) is independent of W. By analyzing how and where fˆ(x;⋅,α) blows up in λ, a...

In this paper, we obtain the moderate deviation principles for Engel’s series, Sylvester’s series and Cantor’s products, which is a complement to Zhu (2014).