Multi-level Monte Carlo methods for the approximation of invariant measures of stochastic differential equations

We develop a framework that allows the use of the multi-level Monte Carlo (MLMC) methodology (Giles in Acta Numer. 24:259–328, 2015. https://doi.org/10.1017/S096249291500001X) to calculate expectations with respect to the invariant measure of an ergodic SDE. In that context, we study the (over-damped) Langevin equations with a strongly concave potential. We show that when appropriate contracting couplings for the numerical integrators are available, one can obtain a uniform-in-time estimate of the MLMC variance in contrast to the majority of the results in the MLMC literature. As a consequence, a root mean square error of $$\mathcal {O}(\varepsilon )$$ is achieved with $$\mathcal {O}(\varepsilon ^{-2})$$ complexity on par with Markov Chain Monte Carlo (MCMC) methods, which, however, can be computationally intensive when applied to large datasets. Finally, we present a multi-level version of the recently introduced stochastic gradient Langevin dynamics method (Welling and Teh, in: Proceedings of the 28th ICML, 2011) built for large datasets applications. We show that this is the first stochastic gradient MCMC method with complexity $$\mathcal {O}(\varepsilon ^{-2}|\log {\varepsilon }|^{3})$$, in contrast to the complexity $$\mathcal {O}(\varepsilon ^{-3})$$ of currently available methods. Numerical experiments confirm our theoretical findings.     

A RATHER INHUMANE ARRANGEMENT: SOUTHEAST ASIAN SETTLEMENT ASSISTANCE INITIATIVES IN MELBOURNE

Due to its specific historical context and unique sociopolitical milieu, Australia has developed a relatively distinctive Southeast Asian settlement assistance model. This article explores the adequacy of the pattern of service delivery that has evolved in Melbourne in response to the settlement needs of the Southeast Asian community. The research finds that the Australian Indochinese aid initiative is high on principle and rhetoric and low on practical solutions. Despite compassionate public pronouncements, assistance institutions increasingly operate in a harsh social, economic, and political context wherein there are few forced migrant-specific provisions. A devolution policy has also engendered an inefficient patchwork service setup rather than a benevolent resettlement arrangement. Without a more genuine official orientation and a more appropriate overall approach, many Australian Southeast Asians are destined to continue a protracted struggle against disadvantage and neglect.     

Residents' Efforts at Neighborhood Stabilization: Facing the Challenges of Inner-City Neighborhoods

This paper examines the response of residents in one inner-city, racially, and economically diverse neighborhood to a sudden increase in crime, drugs and disorder. Rather than withdrawing, residents in this neighborhood responded by organizing a major collective effort to develop a stabilization plan for the neighborhood. Factors useful in understanding this atypical response include a citywide structure that encourages citizen participation, the city government's commitment to the neighborhood, a history of neighborhood activism, and residents' commitment to the neighborhood. A social movement perspective that examines the nature of successful social movement organizations, the political context of movement activities, and micromovement processes is useful in analyzing cases of neighborhood activism.