Stochastic models associated to a Nonlocal Porous Medium Equation

The nonlocal porous medium equation considered in this paper is a degenerate nonlinear evolution equation involving a space pseudo-differential operator of fractional order. This space-fractional equation admits an explicit, nonnegative, compactly supported weak solution representing a probability density function. In this paper we analyze the link between isotropic transport processes, or random flights, and the nonlocal porous medium equation. In particular, we focus our attention on the interpretation of the weak solution of the nonlinear diffusion equation by means of random flights.Comment: Published at https://doi.org/10.15559/18-VMSTA112 in the Modern Stochastics: Theory and Applications (https://vmsta.org/) by VTeX (http://www.vtex.lt/

A family of random walks with generalized Dirichlet steps

We analyze a class of continuous time random walks in $\mathbb R^d,d\geq 2,$ with uniformly distributed directions. The steps performed by these processes are distributed according to a generalized Dirichlet law. Given the number of changes of orientation, we provide the analytic form of the probability density function of the position $\{\underline{\bf X}_d(t),t>0\}$ reached, at time $t>0$, by the random motion. In particular, we analyze the case of random walks with two steps. In general, it is an hard task to obtain the explicit probability distributions for the process $\{\underline{\bf X}_d(t),t>0\}$ . Nevertheless, for suitable values for the basic parameters of the generalized Dirichlet probability distribution, we are able to derive the explicit conditional density functions of $\{\underline{\bf X}_d(t),t>0\}$. Furthermore, in some cases, by exploiting the fractional Poisson process, the unconditional probability distributions are obtained. This paper extends in a more general setting, the random walks with Dirichlet displacements introduced in some previous papers

Stochastic velocity motions and processes with random time

The aim of this paper is to analyze a class of random motions which models the motion of a particle on the real line with random velocity and subject to the action of the friction. The speed randomly changes when a Poissonian event occurs. We study the characteristic and the moment generating function of the position reached by the particle at time $t>0$. We are able to derive the explicit probability distributions in few cases for which discuss the connections with the random flights. The moments are also widely analyzed. For the random motions having an explicit density law, further interesting probabilistic interpretations emerge if we deal with them varying up a random time. Essentially, we consider two different type of random times, namely Bessel and Gamma times, which contain, as particular cases, some important probability distributions (e.g. Gaussian, Exponential). In particular, for the random processes built by means of these compositions, we derive the probability distributions fixed the number of Poisson events. Some remarks on the possible extensions to the random motions in higher spaces are proposed. We focus our attention on the persistent planar random motion

Productivity Growth and Disinflation in Chile

This paper analyzes the role productivity growth had on disinflation in Chile during the 1990s. It argues that productivity growth was key in avoiding the output costs of stabilization in a highly indexed economy. Disinflation from the early 1990s through 1998 was costless. Among the many external and domestic factors that contributed to good macroeconomic performance, which combined simultaneously very high rates of growth and declining inflation, productivity stands high. The paper’s simulation results illustrate the latter point.

Exchange Rate Policy in Chile since 1960: Political Economy and the Choice of Regime

This paper analyzes exchange rate policies in Chile since the 1960s. A brief overview of main policies is presented. Particular attention is paid to the two episodes of fixed-exchange rate as well as the reasons why policy makers may have arrived to those decisions. The paper also examines the long Chilean tradition of using a crawling peg to preserve competitiveness and as a quick exit during times of crisis. More specifically, this paper attempts to uncover political economy factors that may have influenced decisions on exchange rate policy. Empirical evidence on the economic environment during different episodes of exchange rate management as well as the political economy factors that may haveinfluenced the options are presented.

Rapid Growth Of Monetary Aggregates And Inflation: The International Evidence

This paper presents empirical evidence for low inflation countries in which M1 has grown persistently for at least one year at rates much higher than the inflation rate. In none of these episodes has there been a similar increase in inflation, as a straightforward application of the simplest version of the quantity theory of money would suggest. This evidence confirms the idea that even in a world of long-run neutrality of money, the use of monetary aggregates to conduct monetary policy could be highly misleading.