Abstract In this paper, we tame the uncertainty about volatility in time-averaging principle for stochastic differential equations driven by G-Brownian motion (G-SDEs) based on Lyapunov condition. That means treat condition presence of a family probability measures, each corresponding to different scenario volatility. The main tool mathematical analysis is G-stochastic calculus, which introduce...

The long-lasting controversy on the usefulness of cost-averaging as an investment strategy is revived by the increasingly more aggressive marketing for long term saving plans with new intensity. Albrecht et al. (2002) illustrated using a shortfall risk based approach that cost-averaging may be an efficient strategy compared to simple buy-and-hold-strategies. The contribution of this paper is a ...

Abstract We consider minimizing a smooth and strongly convex objective function using stochastic Newton method. At each iteration, the algorithm is given an oracle access to estimate of Hessian matrix. The model includes popular algorithms such as Subsampled Sketch, which can efficiently construct estimates for many tasks, e.g., training machine learning models. Despite second-order information...

We study the asymptotic behavior for an inhomogeneous multiscale stochastic dynamical system with non-smooth coefficients. Depending on averaging regime and homogenization regime, two strong convergences in principle of functional law large numbers type are established. Then we consider small fluctuations around its average. Nine cases central limit theorems obtained. In particular, even though...

We propose a new stochastic search algorithm for Gaussian graphical models called the mode oriented stochastic search. Our algorithm relies on the existence of a method to accurately and efficiently approximate the marginal likelihood associated with a graphical model when it cannot be computed in closed form. To this end, we develop a new Laplace approximation method to the normalizing constan...

This paper considers convex optimization problems where nodes of a network have access to summands of a global objective. Each of these local objectives is further assumed to be an average of a finite set of functions. The motivation for this setup is to solve large scale machine learning problems where elements of the training set are distributed to multiple computational elements. The decentr...