Asymptotic normality and efficiency of the maximum likelihood estimator for the parameter of a ballistic random walk in a random environment

We consider a one dimensional ballistic random walk evolving in a parametric independent and identically distributed random environment. We study the asymptotic properties of the maximum likelihood estimator of the parameter based on a single observation of the path till the time it reaches a distant site. We prove an asymptotic normality result for this consistent estimator as the distant site tends to infinity and establish that it achieves the Cram\'er-Rao bound. We also explore in a simulation setting the numerical behaviour of asymptotic confidence regions for the parameter value

Maximum likelihood estimation in the context of a sub-ballistic random walk in a parametric random environment

We consider a one dimensional sub-ballistic random walk evolving in a parametric i.i.d. random environment. We study the asymptotic properties of the maximum likelihood estimator (MLE) of the parameter based on a single observation of the path till the time it reaches a distant site. In that purpose, we adapt the method developed in the ballistic case by Comets et al (2014) and Falconnet, Loukianova and Matias (2014). Using a supplementary assumption due to the specificity of the sub-ballistic regime, we prove consistency and asymptotic normality as the distant site tends to infinity. To emphazis the role of the additional assumption, we investigate the Temkin model with unknown support, and it turns out that the MLE is consistent but, unlike in the ballistic regime, the Fisher information is infinite. We also explore the numerical performance of our estimation procedure.Comment: arXiv admin note: text overlap with arXiv:1302.042

Clouds of Suspicion: Airspace Arrangements, Escalation, and Discord in U.S./NATO-Russian Relations

Policy makers in the Euro-Atlantic region are concerned that incidents involving military or civilian aircraft could result in dangerous escalation of conflict between Russia and the West. This brief introduces the policy problem and traces the evolution of three sets of cooperative airspace arrangements developed by Euro-Atlantic states since the end of the Cold War—(1) cooperative aerial surveillance of military activity, (2) exchange of air situational data, and (3) joint engagement of theater air and missile threats—in order to clarify the current regional airspace insecurity dynamics and identify opportunities to promote transparency and confidence in U.S./NATO-Russian relations

Maximum likelihood estimator consistency for recurrent random walk in a parametric random environment with finite support

We consider a one-dimensional recurrent random walk in random environment (RWRE) when the environment is i.i.d. with a parametric, finitely supported distribution. Based on a single observation of the path, we provide a maximum likelihood estimation procedure of the parameters of the environment. Unlike most of the classical maximum likelihood approach, the limit of the criterion function is in general a nondegenerate random variable and convergence does not hold in probability. Not only the leading term but also the second order asymptotics is needed to fully identify the unknown parameter. We present different frameworks to illustrate these facts. We also explore the numerical performance of our estimation procedure

Cooperative Airspace Security in the Euro-Atlantic Region

This paper offers an overview of existing arrangements and provides a discussion of policy challenges involved in constructing a regional Euro-Atlantic capability to jointly monitor and counter common airspace threats through the networking of military and civil air traffic control systems. It argues that a strengthened political, financial, and technical commitment to build a cooperative airspace security system is a “win-win” area for NATO-Russian engagement that would promote regional military transparency, deepen cooperation against airborne terrorism, and enhance regional crisis stability. Deeper and broader regional airspace security arrangements would also foster the culture of cooperation, transparency, and confidence built between all Euro-Atlantic states—large and small—through practical civil-military cooperation. In a May 2010 op-ed, U.S. Vice President Joseph Biden wrote of the “vital” need to “adapt” Euro-Atlantic security institutions “to the challenges—and opportunities—of a new era.” He noted the importance of “reciprocal transparency” of military forces, called for improved cooperative means to deal with “external challenges,” argued for more “effective conflict-prevention, conflict-management, and crisis-resolution” mechanisms to enhance stability, and reaffirmed the importance of territorial integrity and the indivisibility of regional security. “We seek an open and increasingly united Europe in which all countries, including Russia, play their full roles,” Biden stated. A careful examination of “bottom-up” cooperative opportunities in airspace security in line with this vision is in order at a time when policy makers in Washington, Brussels, and Moscow seek to design and agree on a common capability to defend the Euro-Atlantic against missile threats. Toward this end, an expansion of ongoing cooperative airspace security projects is a cost-effective and technically feasible undertaking that could promote both agreement and action on the rules of engagement, as well as on the sharing of information, technology, and costs in regional missile defense that involves Russia. In an effort to make Euro-Atlantic security “indivisible,” it might also be useful to learn from past experience with using this type of functional engagement for the purposes of reassurance. This paper begins by introducing a practical case of airspace problems over the Baltic. It continues with an overview of existing North Atlantic Treaty Organization (NATO) approaches to the networking of military and civil air traffic control systems. It further describes the William J. Clinton administration’s efforts to build cooperation in Central and Eastern Europe through the Regional Airspace Initiative. The paper then offers an analysis of present airspace tensions in conflict-prone and non-NATO state areas in the region. Finally, it reviews the ongoing NATO-Russian Cooperative Airspace Initiative and recommends that this project be expanded geographically and to the sharing of military aircraft data as well as extended to U.S.-Russia counterterrorism cooperation across the Bering Strait