13,783 research outputs found
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
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 reached, at time
, 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 . 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 . 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 . 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.
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