Related papers: Potentials of stable processes
The stability of the Standard Model is determined by the true minimum of the effective Higgs potential. We show that the potential at its minimum when computed by the traditional method is strongly dependent on the gauge parameter. It…
A new family of stable processes indexed by metric spaces with stationary increments are introduced. They are special cases of a new family of set-indexed stable processes with Chentsov representation. At the heart of the representation, a…
We propose a novel group of Gaussian Process based algorithms for fast approximate optimal stopping of time series with specific applications to financial markets. We show that structural properties commonly exhibited by financial time…
This note is devoted to study the output stabilizability of a simplified and a one-dimensional diffusion equation. Necessary and sufficient conditions for the system to be output stabilizable will be given. These conditions are given in…
We study the statistics of infima, stopping times and passage probabilities of entropy production in nonequilibrium steady states, and show that they are universal. We consider two examples of stopping times: first-passage times of entropy…
The speed limits on entanglement are defined as the maximal rate at which entanglement can be generated or degraded in a physical process. We derive the speed limits on entanglement, using the relative entropy of entanglement and…
Because of their tractability and their natural interpretations in term of market quantities, Hawkes processes are nowadays widely used in high-frequency finance. However, in practice, the statistical estimation results seem to show that…
We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling…
The problem is a power-law asymptotics of the probability that a self-similar process does not exceed a fixed level during long time. The exponent in such asymptotics is estimated for some Gaussian processes, including the fractional…
This paper considers a simulation-based estimator for a general class of Markovian processes and explores some strong consistency properties of the estimator. The estimation problem is defined over a continuum of invariant distributions…
We consider the Markov chain approximations for singular stable-like processes. First we obtain properties of some Markov chains. Then we construct the approximating Markov chains and give a necessary condition for weak convergence of these…
We study a problem when a solution to optimal stopping problem for one-dimensional diffusion will generate by threshold strategy. Namely, we give necessary and sufficient conditions under which an optimal stopping time can be specified as…
In this work, we consider systems that are subjected to intermittent instabilities due to external stochastic excitation. These intermittent instabilities, though rare, have a large impact on the probabilistic response of the system and…
Max-stable processes have proved to be useful for the statistical modelling of spatial extremes. Several representations of max-stable random fields have been proposed in the literature. One such representation is based on a limit of…
In this paper, we prove convergence in distribution of Langevin processes in the overdamped asymptotics. The proof relies on the classical perturbed test function (or corrector) method, which is used both to show tightness in path space,…
In this paper we analyze the behavior of system approximation processes for stable linear time-invariant (LTI) systems and signals in the Paley-Wiener space PW_\pi^1. We consider approximation processes, where the input signal is not…
We study the statistics of the maximum and minimum of a set of $N$ random variables whose dynamical and statistical properties fall within the scope of infinite ergodic theory. These non-stationary yet recurrent systems are described, in…
We present sufficient conditions for the transience and the existence of local times of a Feller process, and the ultracontractivity of the associated Feller semigroup; these conditions are sharp for L\'{e}vy processes. The proof uses a…
Under an appropriate regular variation condition, the affinely normalized partial sums of a sequence of independent and identically distributed random variables converges weakly to a non-Gaussian stable random variable. A functional version…
A natural criticism of the optimal protocol of the irreversible work found for weakly driven processes is its experimental difficulty in being implementable due to its singular part. In this work, I explore the possibility of taking its…