A note on randomly scaled scale-decorated Poisson point processes

Randomly scaled scale-decorated Poisson point process is introduced recently in Bhattacharya et al. [2017] where it appeared as weak limit of a sequence of point processes in the context of branching random walk. In this article, we obtain a characterization for these processes based on scaled-Laplace functional. As a consequence, we obtain a characterization for strictly $\alpha$-stable point process (also known as scale-decorated Poisson point process) based on scaled-Laplace functional . a connection with randomly shifted decorated Poisson point process is obtained. The tools and approach used e very similar to those in Subag and Zeitouni [2015].Comment: 12 page

Arbitrage from a Bayesian's Perspective

This paper builds a model of interactive belief hierarchies to derive the conditions under which judging an arbitrage opportunity requires Bayesian market participants to exercise their higher-order beliefs. As a Bayesian, an agent must carry a complete recursion of priors over the uncertainty about future asset payouts, the strategies employed by other market participants that are aggregated in the price, other market participants' beliefs about the agent's strategy, other market participants beliefs about what the agent believes their strategies to be, and so on ad infinitum. Defining this infinite recursion of priors -- the belief hierarchy so to speak -- along with how they update gives the Bayesian decision problem equivalent to the standard asset pricing formulation of the question. The main results of the paper show that an arbitrage trade arises only when an agent updates his recursion of priors about the strategies and beliefs employed by other market participants. The paper thus connects the foundations of finance to the foundations of game theory by identifying a bridge from market arbitrage to market participant belief hierarchies

Persistence of heavy-tailed sample averages occurs by infinitely many jumps

We consider the sample average of a centered random walk in $\mathbb{R}^d$ with regularly varying step size distribution. For the first exit time from a compact convex set $A$ not containing the origin, we show that its tail is of lognormal type. Moreover, we show that the typical way for a large exit time to occur is by having a number of jumps growing logarithmically in the scaling parameter.Comment: 25 pages, 2 figure

Point process convergence for branching random walks with regularly varying steps

We consider the limiting behaviour of the point processes associated with a branching random walk with supercritical branching mechanism and balanced regularly varying step size. Assuming that the underlying branching process satisfies Kesten-Stigum condition, it is shown that the point process sequence of properly scaled displacements coming from the n-th generation converges weakly to a Cox cluster process. In particular, we establish that a conjecture of Brunet and Derrida (2011) remains valid in this setup, investigate various other issues mentioned in their paper and recover the main result of Durrett (1983) in our framework.Comment: 22 pages, 2 figures, To appear in Annales de l'Institut Henri Poincar\'e (B) Probabilit\'es et Statistiques, Proof of Lemma 3.4 differs from previous versio

Large deviation for extremes of branching random walk with regularly varying displacements

We consider discrete time branching random walk on real line where the displacements of particles coming from the same parent are allowed to be dependent and jointly regularly varying. Using the one large bunch asymptotics, we derive large deviation for the extremal processes associated to the suitably scaled positions of particles in the nth generation where the genealogical tree satisfies Kesten-Stigum condition. The large deviation limiting measure in this case is identified in terms of the cluster Poisson point process obtained in the underlying weak limit of the point processes. As a consequence of this, we derive large deviation for the rightmost particle in the nth generation giving the heavy-tailed analogue of recent work by Gantert and Höfelsauer [2018]

A large sample test for the length of memory of stationary symmetric stable random fields via nonsingular Zd-actions

Based on the ratio of two block maxima, we propose a large sample test for the length of memory of a stationary symmetric α-stable discrete parameter random field. We show that the power function converges to 1 as the sample-size increases to ∞ under various classes of alternatives having longer memory in the sense of Samorodnitsky (2004). Ergodic theory of nonsingular Zd-actions plays a very important role in the design and analysis of our large sample test

Polariton Emission Characteristics of a Modulation-Doped Multiquantum-Well Microcavity Diode

The role of polariton-electron scattering on the performance characteristics of an electrically injected GaAs-based quantum well microcavity diode in the strong coupling regime has been investigated. An electron gas is introduced in the quantum wells by modulation doping with silicon dopants. It is observed that polariton-electron scattering suppresses the relaxation bottleneck in the lower polariton branch. However, it is not adequate to produce a degenerate coherent condensate at k|| ~ 0 and coherent emission.Comment: 14 pages, 4 figures, submitted to Applied Physics Letter