Consistency of the Tikhonov’s regularization in an ill-posed problem with α-mixing random data

In this article, we establish exponential inequalities for the probability of the distance between the approximated solution and the exact one for an operator equation with an exact right-hand side. In addition, the second member of the operator equation is observed with α-mixing random errors. These inequalities yield the almost complete convergence of the approximate solution.     

An integrated relapse prevention and relationship safety intervention for women on methadone: testing short-term effects on intimate partner violence and substance use

This study tests the feasibility, safety, and short-term preliminary effects of a relapse prevention and relationship safety (RPRS) intervention in reducing drug use and the experience of intimate partner violence (IPV) among women on methadone. For this randomized controlled trial, 34 women who met IPV and drug use criteria were randomly assigned to either the RPRS condition (n = 16) or a one-session informational control (IC) condition (n = 18). RPRS participants were more likely than IC participants to report a decrease in minor physical or sexual IPV (OR = 7.1, p = .05), minor psychological IPV (OR = 5.3, p = .03) and severe psychological IPV (OR = 6.07, p = .03) at the 3-month follow-up. Data suggest that RPRS participants were also more likely than IC participants to report a decrease in any drug use at 3 months (OR = 3.3, p = .08). This study provides preliminary evidence that the RPRS intervention is effective in reducing IPV and drug use among women on methadone.     

On the rate of convergence of the Robbins–Monro's algorithm in a linear stochastic ill-posed problem with α-mixing data

In this paper we consider a recursive method of Robbins–Monro type to estimate the solution of the linear problem Ax = u, in which the second member is measured with α-mixing errors. We also show the almost complete convergence (a.co) of this algorithm specifying its convergence rate.