Related papers: A note on the Cobb-Douglas function
We introduce a functional domain of attraction approach for stochastic processes, which is more general than the usual one based on weak convergence. The distribution function G of a continuous max-stable process on [0,1] is introduced and…
The covariance function of a Gauss-Markov process evaluated at points $(s,t)$ admits a representation as a product of a function of $\min(s,t)$ and a function of $\max(s,t)$. We call these functions the covariance factors of a Gauss-Markov…
If there is a topologically locally constant family of smooth algebraic varieties together with an admissible normal function on the total space, then the latter is constant on any fiber if this holds on some fiber. Combined with spreading…
The condition number of a differentiable convex function, namely the ratio of its smoothness to strong convexity constants, is closely tied to fundamental properties of the function. In particular, the condition number of a quadratic convex…
Out of the companies, Dolby is the company with the best overall financial and operation health. According to the table that accounted its financial statements for the past three years, Dolby has stable profit margins that generates a…
Labor share, the fraction of economic output accrued as wages, is inexplicably declining in industrialized countries. Whilst numerous prior works attempt to explain the decline via economic factors, our novel approach links the decline to…
A loss function measures the discrepancy between the true values (observations) and their estimated fits, for a given instance of data. A loss function is said to be proper (unbiased, Fisher consistent) if the fits are defined over a unit…
It is well-known that selling different goods in a single bundle can significantly increase revenue. However, bundling is no longer profitable if the goods have high production costs. To overcome this challenge, we introduce a new…
In this note, we discuss a class of time-dependent Hamilton-Jacobi equations depending on a function of time, this function being chosen in order to keep the maximum of the solution to the constant value 0. The main result of the note is…
In this short note, we will strengthen the classic Doob's $L^p$ inequality for sub-martingale processes. Because this inequality is of fundamental importance to the theory of stochastic process, we believe this generalization will find many…
The self-concordant-like property of a smooth convex function is a new analytical structure that generalizes the self-concordant notion. While a wide variety of important applications feature the self-concordant-like property, this concept…
In this work, we aim to study a strong version of Ito's lemma for convex function. By considering the corresponding sub-martingale on a Brownian motion, we gain more insights about the convex function through a probabilistic viewpoint. The…
We present a quantitative theory for a relaxation function in a simple glass-forming model (binary mixture of particles with different interaction parameters). It is shown that the slowing down is caused by the competition between locally…
A common assumption of political economy is that profit rates across firms or sectors tend to uniformity, and often models are formulated in which this tendency is assumed to have been realised. But in reality this tendency is never…
Real-time price signals and power generation levels (disaggregated or aggregated) are commonly made available to the public by Independent System Operators (ISOs) to promote efficiency and transparency. However, they may inadvertently…
The Douglas-Rachford algorithm is a classical and powerful splitting method for minimizing the sum of two convex functions and, more generally, finding a zero of the sum of two maximally monotone operators. Although this algorithm is well…
On a finite outcome space, the canonical Gibbs distribution is usually obtained by maximizing Shannon entropy at fixed mean of an externally supplied energy functional. This paper studies the finite-state consequences of a ratio-cost…
We characterize the complete monotonicity of the Kilbas-Saigo function on the negative half-line. We also provide the exact asymptotics at $-\infty$, and uniform hyperbolic bounds are derived. The same questions are addressed for the…
We study the estimation of a stable Cox-Ingersoll-Ross model, which is a special subcritical continuous-state branching process with immigration. The process is characterized in terms of some stochastic equations. The exponential ergodicity…
This article concerns the optimal choice of flat taxes on labor and capital income, and on consumption, in a tractable economic model in which agents are subject to idiosyncratic investment risk. We identify the tax rates which maximize…