Subgeometric rates of convergence for a class of continuous-time Markov process

Let (Phi(t))(t is an element of R+) be a Harris ergodic continuous-time Markov process on a general state space, with invariant probability measure pi. We investigate the rates of convergence of the transition function P-t(x, (.)) to pi; specifically, we find conditions under which r(t) vertical bar vertical bar P-t (x, (.)) - pi vertical bar vertical bar -> 0 as t -> infinity, for suitable subgeometric rate functions r(t), where vertical bar vertical bar - vertical bar vertical bar denotes the usual total variation norm for a signed measure. We derive sufficient conditions for the convergence to hold, in terms of the existence of suitable points on which the first hitting time moments are bounded. In particular, for stochastically ordered Markov processes, explicit bounds on subgeometric rates of convergence are obtained. These results are illustrated in several examples.

Post-Fordism, the welfare state and the personal social services: A comparison of Australia and Britain

The Post-Fordist welfare state thesis locates contemporary social welfare change within a wider analysis of the transformation of capitalist accumulation regimes. Whilst this analysis is useful in directing attention to macro socio-economic change, it has for the most part contained three shortcomings. First, the Post-Fordist thesis has overemphasized the role of historical 'breaks' in the development of social welfare as it purportedly passes from Fordism to Post-Fordism. Second, the thesis has assumed a degree of convergence between welfare states as a result of global economic forces. In doing so, it has underemphasized the mediating impact of existing institutional arrangements within nations. Third, the thesis has assumed, rather than demonstrated, the specific changes which are alleged to be taking place in various fields of social welfare. As a consequence, aspects of continuity in social welfare have been neglected. These three lacunae are addressed through a comparative analysis of developments in the personal social services in Australia and Britain. Services to older people are employed as the specific context of comparison in relation to three dimensions of measuring transformation along a Post-Fordist trajectory: a shift from a unitary economy to a mixed economy of service provision; changes in the model of service delivery and consumption; and strengthening the governance function of the central state. This comparative analysis suggests the need for refinement of the Post-Fordist welfare state thesis concerning the restructuring of social welfare and its impact on the personal social services.