Related papers: Infinitesimal generators for two-dimensional L\'ev…
In this paper, we study infinite dimensional stochastic systems having both unbounded control and observation operators. First of all, using a semigroup approach, we give another take of the well-posedness of such systems treated in [SIAM…
This paper aims at semi-parametrically estimating the input process to a L\'evy-driven queue by sampling the workload process at Poisson times. We construct a method-of-moments based estimator for the L\'evy process' characteristic…
This study examines a nonparametric inference on a stationary L\'evy-driven Ornstein-Uhlenbeck (OU) process $X = (X_{t})_{t \geq 0}$ with a compound Poisson subordinator. We propose a new spectral estimator for the L\'evy measure of the…
We establish a link between the distribution of an exponential functional I and the undershoots of a subordinator, which is given in terms of the associated harmonic potential measure. This allows us to give a necessary and sufficient…
For many real time applications, it is important to validate the information received from the sensors before entering higher levels of reasoning. This paper presents an any time probabilistic algorithm for validating the information…
We provide asymptotic results and develop high frequency statistical procedures for time-changed L\'evy processes sampled at random instants. The sampling times are given by first hitting times of symmetric barriers whose distance with…
Understanding the generative mechanism of a natural system is a vital component of the scientific method. Here, we investigate one of the fundamental steps toward this goal by presenting the minimal generator of an arbitrary binary Markov…
Last passage times arise in a number of areas of applied probability, including risk theory and degradation models. Such times are obviously not stopping times since they depend on the whole path of the underlying process. We consider the…
Graph generators learn a model from a source graph in order to generate a new graph that has many of the same properties. The learned models each have implicit and explicit biases built in, and its important to understand the assumptions…
Nonparametric methods for the estimation of the Levy density of a Levy process are developed. Estimators that can be written in terms of the ``jumps'' of the process are introduced, and so are discrete-data based approximations. A model…
The widespread adoption of wearable sensors has the potential to provide massive and heterogeneous time series data, driving the use of Artificial Intelligence in human sensing applications. However, data collection remains limited due to…
Multistable L\'evy motions are extensions of L\'evy motions where the stability index is allowed to vary in time. Several constructions of these processes have been introduced recently, based on Poisson and Ferguson-Klass-LePage series…
We develop a new model selection method for the adaptive robust efficient nonparametric signal estimation observed with impulse noise which is defined by the general non Gaussian L\'evy processes. On the basis of the developed method, we…
We consider optimal sensor placement for a family of linear Bayesian inverse problems characterized by a deterministic hyper-parameter. The hyper-parameter describes distinct configurations in which measurements can be taken of the observed…
This article deals with adaptive nonparametric estimation for L\'evy processes observed at low frequency. For general linear functionals of the L\'evy measure, we construct kernel estimators, provide upper risk bounds and derive rates of…
Several two-boundary problems are solved for a special L\'{e}vy process: the Poisson process with an exponential component. The jumps of this process are controlled by a homogeneous Poisson process, the positive jump size distribution is…
L\'evy processes, known for their ability to model complex dynamics with skewness, heavy tails and discontinuities, play a critical role in stochastic modeling across various domains. However, inference for most L\'evy processes, whether in…
The theory of sparse stochastic processes offers a broad class of statistical models to study signals. In this framework, signals are represented as realizations of random processes that are solution of linear stochastic differential…
This paper presents a novel approach to constructing finite generating sets for infinitely generated ideals. By integrating algebraic and computational techniques, we provide a method to identify finite generators, demonstrated through…
We consider the problem of quickly detecting a signal in a sensor network when the subset of sensors in which signal may be present is completely unknown. We formulate this problem as a sequential hypothesis testing problem with a simple…