Non independent continuous-time random walks

The usual development of the continuous-time random walk (CTRW) assumes that jumps and time intervals are a two-dimensional set of independent and identically distributed random variables. In this paper, we address the theoretical setting of nonindependent CTRWs where consecutive jumps and/or time intervals are correlated. An exact solution to the problem is obtained for the special but relevant case in which the correlation solely depends on the signs of consecutive jumps. Even in this simple case, some interesting features arise, such as transitions from unimodal to bimodal distributions due to correlation. We also develop the necessary analytical techniques and approximations to handle more general situations that can appear in practice.

Parrondo-like behavior in continuous-time random walks with memory

The continuous-time random walk (CTRW) formalism can be adapted to encompass stochastic processes with memory. In this paper we will show how the random combination of two different unbiased CTRWs can give rise to a process with clear drift, if one of them is a CTRW with memory. If one identifies the other one as noise, the effect can be thought of as a kind of stochastic resonance. The ultimate origin of this phenomenon is the same as that of the Parrondo paradox in game theory.

Exchange rate predictability

The main goal of this article is to provide an answer to the question: "Does anything forecast exchange rates, and if so, which variables?". It is well known thatexchange rate fluctuations are very difficult to predict using economic models, andthat a random walk forecasts exchange rates better than any economic model (theMeese and Rogoff puzzle). However, the recent literature has identified a series of fundamentals/methodologies that claim to have resolved the puzzle. This article providesa critical review of the recent literature on exchange rate forecasting and illustratesthe new methodologies and fundamentals that have been recently proposed in an up-to-date, thorough empirical analysis. Overall, our analysis of the literature and thedata suggests that the answer to the question: "Are exchange rates predictable?" is,"It depends" -on the choice of predictor, forecast horizon, sample period, model, andforecast evaluation method. Predictability is most apparent when one or more of thefollowing hold: the predictors are Taylor rule or net foreign assets, the model is linear, and a small number of parameters are estimated. The toughest benchmark is therandom walk without drift.

Integro-difference equations for interacting species and the Neolithic transition

We introduce a set of sequential integro-difference equations to analyze the dynamics of two interacting species. Firstly, we derive the speed of the fronts when a species invades a space previously occupied by a second species, and check its validity by means of numerical random-walk simulations. As an example, we consider the Neolithic transition: the predictions of the model are consistent with the archaeological data for the front speed, provided that the interaction parameter is low enough. Secondly, an equation for the coexistence time between the invasive and the invaded populations is obtained for the first time. It agrees well with the simulations, is consistent with observations of the Neolithic transition, and makes it possible to estimate the value of the interaction parameter between the incoming and the indigenous populations

Renewal equations for option pricing

In this paper we will develop a methodology for obtaining pricing expressions for financial instruments whose underlying asset can be described through a simple continuous-time random walk (CTRW) market model. Our approach is very natural to the issue because it is based in the use of renewal equations, and therefore it enhances the potential use of CTRW techniques in finance. We solve these equations for typical contract specifications, in a particular but exemplifying case. We also show how a formal general solution can be found for more exotic derivatives, and we compare prices for alternative models of the underlying. Finally, we recover the celebrated results for the Wiener process under certain limits.

L’impacte de les institucions internacionals sobre la Unió Europea: presa de decisions, integració i europeïtzació

Projecte de recerca elaborat a partir d’una estada a la Center for European Integration de la Freie Universität Berlin, Alemania, entre 2007 i 2009. El tema central del projecte consisteix en la descripció matemàtica de processos espai-temporals mitjançant la teoria dels Continuous-Time Random Walks. L'aportació més significativa del nostre treball en aquest camp consisteix en considerar per primera vegada la interacció entre diversos processos actuant de manera acoblada, ja que fins ara els models existents es limitaven a l'estudi de processos individuals o independents. Aquesta idea fa possible, per exemple, plantejar un sistema de transport en l'espai i a la vegada un procés de reacció (una reacció química, per exemple), i estudiar estadísticament com cada un pot alterar el comportament de l'altre. Això suposa un salt qualitatiu important en la descripció de processos de reacció-dispersió, ja que els nostres models permeten incorporar patrons de dispersió i comportaments temporals (cicles de vida) força realistes en comparació amb els models convencionals. Per tal de completar aquest treball teòric ha estat necessari també desenvolupar algunes eines numèriques (models de xarxa) per facilitar la implementació dels models. En la vessant pràctica, hem aplicat aquestes idees al cas de la dinàmica entre virus i el sistema immunològic que té lloc quan es produeix una infecció a l'organisme. Diferents estudis experimentals portats a terme els últims anys mostren com la resposta immunològica dels organismes superiors presenta una dinàmica temporal força complexa (per exemple, en el cas de la resposta programada). Per aquest motiu, les nostres tècniques matemàtiques són d'especial utilitat per a l'anàlisi d'aquests sistemes. Finalment, altres possibles aplicacions dels models, com ara l'estudi d'invasions biològiques, també han estat considerades.

On the computational security of a distributed key distribution scheme

In a distributed key distribution scheme, a set of servers helps a set of users in a group to securely obtain a common key. Security means that an adversary who corrupts some servers and some users has no information about the key of a noncorrupted group. In this work, we formalize the security analysis of one such scheme which was not considered in the original proposal. We prove the scheme is secure in the random oracle model, assuming that the Decisional Diffie-Hellman (DDH) problem is hard to solve. We also detail a possible modification of that scheme and the one in which allows us to prove the security of the schemes without assuming that a specific hash function behaves as a random oracle. As usual, this improvement in the security of the schemes is at the cost of an efficiency loss.

Optimal taxation without state-contingent debt

To recover a version of Barro's (1979) `random walk'tax smoothing outcome, we modify Lucas and Stokey's (1983) economyto permit only risk--free debt. This imparts near unit root like behaviorto government debt, independently of the government expenditureprocess, a realistic outcome in the spirit of Barro's. We showhow the risk--free--debt--only economy confronts the Ramsey plannerwith additional constraints on equilibrium allocations thattake the form of a sequence of measurability conditions.We solve the Ramsey problem by formulating it in terms of a Lagrangian,and applying a Parameterized Expectations Algorithm tothe associated first--order conditions. The first--order conditions andnumerical impulse response functions partially affirmBarro's random walk outcome. Though the behaviors oftax rates, government surpluses, and government debts differ, allocationsare very close for computed Ramsey policies across incomplete and completemarkets economies.

Accelerated tumor invasion under non-isotropic cell dispersal in glioblastomas

Glioblastomas are highly diffuse, malignant tumors that have so far evaded clinical treatment. The strongly invasive behavior of cells in these tumors makes them very resistant to treatment, and for this reason both experimental and theoretical efforts have been directed toward understanding the spatiotemporal pattern of tumor spreading. Although usual models assume a standard diffusion behavior, recent experiments with cell cultures indicate that cells tend to move in directions close to that of glioblastoma invasion, thus indicating that a biasedrandom walk model may be much more appropriate. Here we show analytically that, for realistic parameter values, the speeds predicted by biased dispersal are consistent with experimentally measured data. We also find that models beyond reaction–diffusion–advection equations are necessary to capture this substantial effect of biased dispersal on glioblastoma spread

Using the HEGY Procedure When Not All Roots Are Present

Empirical studies have shown little evidence to support the presence of all unit roots present in the $^{\Delta_4}$ filter in quarterly seasonal time series. This paper analyses the performance of the Hylleberg, Engle, Granger and Yoo (1990) (HEGY) procedure when the roots under the null are not all present. We exploit the Vector of Quarters representation and cointegration relationship between the quarters when factors $(1-L),(1+L),\bigg(1+L^2\bigg),\bigg(1-L^2\bigg) y \bigg(1+L+L^2+L^3\bigg)$ are a source of nonstationarity in a process in order to obtain the distribution of tests of the HEGY procedure when the underlying processes have a root at the zero, Nyquist frequency, two complex conjugates of frequency $^{\pi/2}$ and two combinations of the previous cases. We show both theoretically and through a Monte-Carlo analysis that the t-ratios $^{t_{{\hat\pi}_1}}$ and $^{t_{{\hat\pi}_2}}$ and the F-type tests used in the HEGY procedure have the same distribution as under the null of a seasonal random walk when the root(s) is/are present, although this is not the case for the t-ratio tests associated with unit roots at frequency $^{\pi/2}$.

Using the HEGY Procedure When Not All Roots Are Present

Empirical studies have shown little evidence to support the presence of all unit roots present in the $^{\Delta_4}$ filter in quarterly seasonal time series. This paper analyses the performance of the Hylleberg, Engle, Granger and Yoo (1990) (HEGY) procedure when the roots under the null are not all present. We exploit the Vector of Quarters representation and cointegration relationship between the quarters when factors $(1-L),(1+L),\bigg(1+L^2\bigg),\bigg(1-L^2\bigg) y \bigg(1+L+L^2+L^3\bigg)$ are a source of nonstationarity in a process in order to obtain the distribution of tests of the HEGY procedure when the underlying processes have a root at the zero, Nyquist frequency, two complex conjugates of frequency $^{\pi/2}$ and two combinations of the previous cases. We show both theoretically and through a Monte-Carlo analysis that the t-ratios $^{t_{{\hat\pi}_1}}$ and $^{t_{{\hat\pi}_2}}$ and the F-type tests used in the HEGY procedure have the same distribution as under the null of a seasonal random walk when the root(s) is/are present, although this is not the case for the t-ratio tests associated with unit roots at frequency $^{\pi/2}$.

Statistics of depth probed by cw measurement of photons in a turbid medium

Photon migration in a turbid medium has been modeled in many different ways. The motivation for such modeling is based on technology that can be used to probe potentially diagnostic optical properties of biological tissue. Surprisingly, one of the more effective models is also one of the simplest. It is based on statistical properties of a nearest-neighbor lattice random walk. Here we develop a theory allowing one to calculate the number of visits by a photon to a given depth, if it is eventually detected at an absorbing surface. This mimics cw measurements made on biological tissue and is directed towards characterizing the depth reached by photons injected at the surface. Our development of the theory uses formalism based on the theory of a continuous-time random walk (CTRW). Formally exact results are given in the Fourier-Laplace domain, which, in turn, are used to generate approximations for parameters of physical interest.

Quantum critical effects in mean-field glassy systems

We consider the effects of quantum fluctuations in mean-field quantum spin-glass models with pairwise interactions. We examine the nature of the quantum glass transition at zero temperature in a transverse field. In models (such as the random orthogonal model) where the classical phase transition is discontinuous an analysis using the static approximation reveals that the transition becomes continuous at zero temperature.

Effectiveness of pharmacist care in the improvement of adherence to antidepressants: a systematic review and meta-analysis

BACKGROUND: Pharmacists can play a decisive role in the management of ambulatory patients with depression who have poor adherence to antidepressant drugs. OBJECTIVE: To systematically evaluate the effectiveness of pharmacist care in improving adherence of depressed outpatients to antidepressants. METHODS: A systematic review and meta-analysis of randomized controlled trials (RCTs) was conducted. RCTs were identified through electronic databases (MEDLINE, Cochrane Central Register of Controlled Trials, Institute for Scientific Information Web of Knowledge, and Spanish National Research Council) from inception to April 2010, reference lists were checked, and experts were consulted. RCTs that evaluated the impact of pharmacist interventions on improving adherence to antidepressants in depressed patients in an outpatient setting (community pharmacy or pharmacy service) were included. Methodologic quality was assessed and methodologic details and outcomes were extracted in duplicate. RESULTS: Six RCTs were identified. A total of 887 patients with an established diagnosis of depression who were initiating or maintaining pharmacologic treatment with antidepressant drugs and who received pharmacist care (459 patients) or usual care (428 patients) were included in the review. The most commonly reported interventions were patient education and monitoring, monitoring and management of toxicity and adverse effects, adherence promotion, provision of written or visual information, and recommendation or implementation of changes or adjustments in medication. Overall, no statistical heterogeneity or publication bias was detected. The pooled odds ratio, using a random effects model, was 1.64 (95% CI 1.24 to 2.17). Subgroup analysis showed no statistically significant differences in results by type of pharmacist involved, adherence measure, diagnostic tool, or analysis strategy. CONCLUSIONS: These results suggest that pharmacist intervention is effective in the improvement of patient adherence to antidepressants. However, data are still limited and we would recommend more research in this area, specifically outside of the US.

The prevalence of child sexual abuse in community and student samples: A meta-analysis

Background: Studies conducted internationally confirm that child sexual abuse is a much more widespread problem than previously thought, with even the lowest prevalence rates including a large number of victims that need to be taken into account. Objective: To carry out a meta-analysis of the prevalence of child sexual abuse in order to establish an overall international figure. Methods: Studies were retrieved from various electronic databases. The measure of interest was the prevalence of abuse reported in each article, these values being combined via a random effects model. A detailed analysis was conducted of the effects of various moderator variables. Results: Sixty-five articles covering 22 countries were included. The analysis showed that 7.9% of men (7.4% without outliers) and 19.7% of women (19.2% without outliers) had suffered some form of sexual abuse prior to the age of eighteen. Conclusions: The results of the present meta-analysis indicate that child sexual abuse is a serious problem in the countries analysed.