First-passage times for non-Markovian processes

First-passage time statistics for non-Markovian processes have heretofore only been developed for processes driven by dichotomous fluctuations that are themselves Markov. Herein we develop a new method applicable to Markov and non-Markovian dichotomous fluctuations and calculate analytic mean first-passage times for particular examples.

First-passage times for non-Markovian processes: Correlated impacts on a free process

We develop a method to obtain first-passage-time statistics for non-Markovian processes driven by dichotomous fluctuations. The fluctuations themselves need not be Markovian. We calculate analytic first-passage-time distributions and mean first-passage times for exponential, rectangular, and long-tail temporal distributions of the fluctuations.

First-passage times for non-Markovian processes: Correlated impacts on bound processes

Our previously developed stochastic trajectory analysis technique has been applied to the calculation of first-passage time statistics of bound processes. Explicit results are obtained for linearly bound processes driven by dichotomous fluctuations having exponential and rectangular temporal distributions.

Bistability driven by Gaussian colored noise: First-passage times

Herein we present a calculation of the mean first-passage time for a bistable one-dimensional system driven by Gaussian colored noise of strength D and correlation time ¿c. We obtain quantitative agreement with experimental analog-computer simulations of this system. We disagree with some of the conclusions reached by previous investigators. In particular, we demonstrate that all available approximations that lead to a state-dependent diffusion coefficient lead to the same result for small D¿c.

First-passage times for non-Markovian processes: Shot noise

The stochastic-trajectory-analysis technique is applied to the calculation of the mean¿first-passage-time statistics for processes driven by external shot noise. Explicit analytical expressions are obtained for free and bound processes.

First-passage times for non-Markovian processes: Multivalued noise

A new method for the calculation of first-passage times for non-Markovian processes is presented. In addition to the general formalism, some familiar examples are worked out in detail.

Life Times, Summer 2009

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Long-tailed trapping times and Lévy flights in a self-organized critical granular system

We present a continuous time random walk model for the scale-invariant transport found in a self-organized critical rice pile [K. Christensen et al., Phys. Rev. Lett. 77, 107 (1996)]. From our analytical results it is shown that the dynamics of the experiment can be explained in terms of Lvy flights for the grains and a long-tailed distribution of trapping times. Scaling relations for the exponents of these distributions are obtained. The predicted microscopic behavior is confirmed by means of a cellular automaton model.

Mean first-passage times for systems driven by gamma and McFadden dichotomous noise

We consider mean first-passage times (MFPTs) for systems driven by non-Markov gamma and McFadden dichotomous noises. A simplified derivation is given of the underlying integral equations and the theory for ordinary renewal processes is extended to modified and equilibrium renewal processes. The exact results are compared with the MFPT for Markov dichotomous noise and with the results of Monte Carlo simulations.

Mean first-passage times for systems driven by equilibrium persistent-periodic dichotomous noise

In a recent paper, [J. M. Porrà, J. Masoliver, and K. Lindenberg, Phys. Rev. E 48, 951 (1993)], we derived the equations for the mean first-passage time for systems driven by the coin-toss square wave, a particular type of dichotomous noisy signal, to reach either one of two boundaries. The coin-toss square wave, which we here call periodic-persistent dichotomous noise, is a random signal that can only change its value at specified time points, where it changes its value with probability q or retains its previous value with probability p=1-q. These time points occur periodically at time intervals t. Here we consider the stationary version of this signal, that is, equilibrium periodic-persistent noise. We show that the mean first-passage time for systems driven by this stationary noise does not show either the discontinuities or the oscillations found in the case of nonstationary noise. We also discuss the existence of discontinuities in the mean first-passage time for random one-dimensional stochastic maps.

One Stop Reentry Reduces Disproportionate Representation, Data Download, Iowa Department of Corrections, January 2011

In a national study released in 2007 by The Sentencing Project, Iowa tops the nation for imprisoning African Americans at a rate of 13.6 times that of whites. In addition, African Americans in Iowa are much more likely to be unemployed, lacking a high school diploma, and earning less than white Iowans. And African American offenders’ return-to-prison rates are higher than for white offenders.

Social Investment Policies in Times of Permanent Austerity

The objective of this paper is to identify the political conditions that are most likely to be conducive to the development of social investment policies. It starts from the view put forward by theorists of welfare retrenchment that in the current context of permanent austerity, policy is likely to be dominated by retrenchment and implemented in a way that allows governments to minimise the risk of electoral punishment (blame avoidance). It is argued that this view is inconsistent with developments observed in several European countries, were some welfare state expansion has taken place mostly in the fields of childcare and active labour market policy. An alternative model is put forward, that emphasises the notion of "affordable credit claiming". It is argued that even under strong budgetary pressures, governments maintain a preference for policies that allow them to claim credit for their actions. Since the traditional redistributive policies tend to be off the menu for cost reasons, governments have tended to favour investments in childcare and active labour market policy as credit claiming tools. Policies developed in this way while they have a social investment flavour, tend to be rather limited in the extent to which they genuinely improve prospects of disadvantaged people by investing in their human capital. A more ambitious strategy of social investment sees unlikely to develop on the basis of affordable credit claiming. The paper starts by presenting the theoretical argument, which is then illustrated with examples taken from European countries both in the pre-crisis and in the post-crisis years.