Large deviations for multidimensional state-dependent shot noise processes

Shot noise processes are used in applied probability to model a variety of physical systems in, for example, teletraffic theory, insurance and risk theory and in the engineering sciences. In this work we prove a large deviation principle for the sample-paths of a general class of multidimensional state-dependent Poisson shot noise processes. The result covers previously known large deviation results for one dimensional state-independent shot noise processes with light tails. We use the weak convergence approach to large deviations, which reduces the proof to establishing the appropriate convergence of certain controlled versions of the original processes together with relevant results on existence and uniqueness

Linear Stochastic Fluid Networks: Rare-Event Simulation and Markov Modulation

We consider a linear stochastic fluid network under Markov modulation, with a focus on the probability that the joint storage level attains a value in a rare set at a given point in time. The main objective is to develop efficient importance sampling algorithms with provable performance guarantees. For linear stochastic fluid networks without modulation, we prove that the number of runs needed (so as to obtain an estimate with a given precision) increases polynomially (whereas the probability under consideration decays essentially exponentially); for networks operating in the slow modulation regime, our algorithm is asymptotically efficient. Our techniques are in the tradition of the rare-event simulation procedures that were developed for the sample-mean of i.i.d. one-dimensional light-tailed random variables, and intensively use the idea of exponential twisting. In passing, we also point out how to set up a recursion to evaluate the (transient and stationary) moments of the joint storage level in Markov-modulated linear stochastic fluid networks

Isolating the chiral contribution in optical two-dimensional chiral spectroscopy using linearly polarized light

The full development of mono- or multi-dimensional time-resolved spectroscopy techniques incorporating optical activity signals has been strongly hampered by the challenge of identifying the small chiral signals over the large achiral background. Here we propose a new methodology to isolate chiral signals removing the achiral background from two commonly used configurations for performing two dimensional optical spectroscopy, known as BOXCARS and GRadient Assisted Photon Echo Spectroscopy (GRAPES). It is found that in both cases an achiral signal from an isotropic system can be completely eliminated by small manipulations of the relative angles between the linear polarizations of the four input laser pulses. Starting from the formulation of a perturbative expansion of the signal in the angle between the beams and the propagation axis, we derive analytic expressions that can be used to estimate how to change the polarization angles of the four pulses to minimize achiral contributions in the studied configurations. The generalization to any other possible experimental configurations has also been discussed. %We derive analytic expressions to changes required to the polarizations in terms of a perturbative expansion in the angle between the beams and the colinear axis. We also numerically estimate higher order coefficients which cover arbitrarily large angles and thus any experimental configuration.Comment: 7 figure

Nonparametric estimation of mark's distribution of an exponential Shot-noise process

In this paper, we consider a nonlinear inverse problem occurring in nuclear science. Gamma rays randomly hit a semiconductor detector which produces an impulse response of electric current. Because the sampling period of the measured current is larger than the mean inter arrival time of photons, the impulse responses associated to different gamma rays can overlap: this phenomenon is known as pileup. In this work, it is assumed that the impulse response is an exponentially decaying function. We propose a novel method to infer the distribution of gamma photon energies from the indirect measurements obtained from the detector. This technique is based on a formula linking the characteristic function of the photon density to a function involving the characteristic function and its derivative of the observations. We establish that our estimator converges to the mark density in uniform norm at a logarithmic rate. A limited Monte-Carlo experiment is provided to support our findings.Comment: Electronic Journal of Statistics, Institute of Mathematical Statistics and Bernoulli Society, 201

Quantum interference in resonant tunneling and single spin measurements

We consider the resonant tunneling through a multi-level system. It is demonstrated that the resonant current displays quantum interference effects due to a possibility of tunneling through different levels. We show that the interference effects are strongly modulated by a relative phase of states carrying the current. This makes it possible to use these effects for measuring the phase difference between resonant states in quantum dots. We extend our model for a description of magnetotransport through the Zeeman doublets. It is shown that, due to spin-flip transitions, the quantum interference effects generate a distinct peak in the shot-noise power spectrum at the frequency of Zeeman splitting. This mechanism explains modulation in the tunneling current at the Larmor frequency observed in scanning tunneling microscope experiments and can be utilized for a single spin measurement.Comment: Some corrections are made. This paper is based on work presented at the 2004 IEEE NTC Quantum Device Technology Worksho

Non-Gaussian Process Regression

Standard GPs offer a flexible modelling tool for well-behaved processes. However, deviations from Gaussianity are expected to appear in real world datasets, with structural outliers and shocks routinely observed. In these cases GPs can fail to model uncertainty adequately and may over-smooth inferences. Here we extend the GP framework into a new class of time-changed GPs that allow for straightforward modelling of heavy-tailed non-Gaussian behaviours, while retaining a tractable conditional GP structure through an infinite mixture of non-homogeneous GPs representation. The conditional GP structure is obtained by conditioning the observations on a latent transformed input space and the random evolution of the latent transformation is modelled using a L\'{e}vy process which allows Bayesian inference in both the posterior predictive density and the latent transformation function. We present Markov chain Monte Carlo inference procedures for this model and demonstrate the potential benefits compared to a standard GP

Laser diagnostics and minor species detection in combustion using resonant four-wave mixing

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