Continuous-time random walks with reset events: Historical background and new perspectives

In this paper, we consider a stochastic process that may experience random reset events which relocate the system to its starting position. We focus our attention on a one-dimensional, monotonic continuous-time random walk with a constant drift: the process moves in a fixed direction between the reset events, either by the effect of the random jumps, or by the action of a deterministic bias. However, the orientation of its motion is randomly determined after each restart. As a result of these alternating dynamics, interesting properties do emerge. General formulas for the propagator as well as for two extreme statistics, the survival probability and the mean first-passage time, are also derived. The rigor of these analytical results is verified by numerical estimations, for particular but illuminating examples.Comment: 11 pages, 5 figure

Bolivia: Impact of shocks and poverty policy on household welfare

This paper evaluates the short term impacts on poverty of pro-poor expenditure and total social expenditure during the 1999-2002 period of Bolivian economic recession. Observed characteristics of recession are simulated by the combined effects of negative terms of trade shock, reduction in foreign saving flows and low output growth. Evaluation is performed by simulating the impacts of shocks and social expenditures in an environment of low growth: i) on macro aggregates of consumption, income, saving and prices (based on a simple static 1-2-3 model built with 1998 data as the base year), ii) on household income and consumption levels by quintiles and areas, and iii) on consumption based poverty indicators by areas. The following were main results from experiments: The terms of trade shock had greater negative impact on household income then reduction in foreign saving flows. In contrast, reduction in foreign saving flows had greater negative impact on household consumption then the terms of trade shock. Poverty measured by the head count ratio has been greater from reduction in foreign saving flows then from the terms of trade shock. Poverty measured by the poverty gap and poverty intensity has concentrated in rural areas, being greater from reduction in foreign saving flows then from the terms of trade shock. Under macroeconomic stability (no shocks and 1998 macro conditions) social expenditure policy for poverty reduction would have had an important positive impact on household income and consumption levels (more so in income then consumption), in reducing the number of poor (more in urban then rural areas), and in reducing poverty gap and poverty intensity (more so in rural areas). However, social expenditure policy does not promote the production of tradables. The combined positive effects from observed social expenditure policy and effort in an environment of low output growth, did not compensate the combined negative impacts from the experienced terms of trade shock and reduction in foreign saving flows. These conclusions show that under macroeconomic disequilibrium poverty reduction efforts become policies of poverty containment or safety net programs. Poverty reduction is a long term objective that requires long term commitment for an environment on macroeconomic stability.External Shocks; Poverty; CGEM 1-2-3; HEGY

The Elasticity of Substitution in Demand for Non-Tradable Goods in Bolivia

This paper uses a CES function to estimate the constant elasticity of substitution in consumption for non-tradables relative to tradables in a dependent economy framework. The methodology for generating data on real consumption of tradable and non-tradable goods, real prices of tradable and non-tradable goods and real absorption is based on the Bolivian Input-Output Matrix, producing quarterly data for the period 1990. 1 to 2002. 4. The data identify Bolivia as a country highly open to trade, with an average ratio of 55 percent in the value of exports and imports relative to GDP, non-tradable production accounting for 52 percent of GDP, and differences in the behavior of the internal and external real exchange rates. The HEGY test is used to identify and separate out seasonal unit roots in the data. A cointegration relationship was found between real absorption, the non-tradable to tradable consumption ratio and the non-tradable to tradable price ratio, suggesting inelasticity of substitution.

Solvability of the Direct and Inverse Problems for the Nonlinear Schrödinger Equation

In this paper we study rigorous spectral theory and solvability for both the direct and inverse problems of the Dirac operator associated with the nonlinear Schrödinger equation. We review known results and techniques, as well as incorporating new ones, in a comprehensive, unified framework. We identify functional spaces in which both direct and inverse problems are well posed, have a unique solution and the corresponding direct and inverse maps are one to one

Exit times in non-Markovian drifting continuous-time random walk processes

By appealing to renewal theory we determine the equations that the mean exit time of a continuous-time random walk with drift satisfies both when the present coincides with a jump instant or when it does not. Particular attention is paid to the corrections ensuing from the non-Markovian nature of the process. We show that when drift and jumps have the same sign the relevant integral equations can be solved in closed form. The case when holding times have the classical Erlang distribution is considered in detail.Comment: 9 pages, 3 color plots, two-column revtex 4; new Appendix and references adde

A Semi-deterministic random walk with resetting

We consider a discrete-time random walk $(x_t)$ which at random times is reset to the starting position and performs a deterministic motion between them. We show that the quantity $\Pr \Big( x_{ t+1}= n+1 |x_{t}=n \Big), n\to \infty$ determines if the system is averse, neutral or inclined towards resetting. It also classifica the stationary distribution. Double barrier probabilities, first passage times and the distribution of the escape time from intervals are determined