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L\'evy processes are widely used in financial mathematics to model return data. Price processes are then defined as a corresponding geometric L\'evy process, implying the fact that returns are independent. In this paper we propose an…
The purpose of this paper is to adapt the empirical characteristic function (ECF) method to stable, but possibly not inverse stable linear stochastic system driven by the increments of a Levy-process. A remarkable property of the ECF method…
L\'evy processes are widely used in financial mathematics, telecommunication, economics, queueing theory and natural sciences for modelling. We propose an essentially asymptotically efficient estimation method for the system parameters of…
Linear dynamical systems, driven by a non-white noise which has the Levy distribution, are analysed. Noise is modelled by a specific stochastic process which is defined by the Langevin equation with a linear force and the Levy distributed…
Calibrating a L\'evy process usually requires characterizing its jump distribution. Traditionally this problem can be solved with nonparametric estimation using the empirical characteristic functions (ECF), assuming certain regularity, and…
Levy processes, which have stationary independent increments, are ideal for modelling the various types of noise that can arise in communication channels. If a Levy process admits exponential moments, then there exists a parametric family…
Recently, extracting data-driven governing laws of dynamical systems through deep learning frameworks has gained a lot of attention in various fields. Moreover, a growing amount of research work tends to transfer deterministic dynamical…
We analyze the statistical performance of identification of stochastic dynamical systems with non-linear measurement sensors. This includes stochastic Wiener systems, with linear dynamics, process noise and measured by a non-linear sensor…
A dynamical model based on a continuous addition of colored shot noises is presented. The resulting process is colored and non-Gaussian. A general expression for the characteristic function of the process is obtained, which, after a scaling…
The objective in stochastic filtering is to reconstruct information about an unobserved (random) process, called the signal process, given the current available observations of a certain noisy transformation of that process. Usually X and Y…
We present a general system identification procedure capable of estimating of a broad spectrum of state-space dynamical models, including linear time-invariant (LTI), linear parameter-varying} (LPV), and nonlinear (NL) dynamics, along with…
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…
We present a finite-time framework for identifying stable and unstable linear time-invariant (LTI) systems from a single closed-loop input-output trajectory. The method does not require knowledge of the stabilizing controller, an…
Literature is full of inference techniques developed to estimate the parameters of stochastic dynamical systems driven by the well-known Brownian noise. Such diffusion models are often inappropriate models to properly describe the dynamics…
This study addresses the challenges in parameter estimation of stochastic differential equations driven by non-Gaussian noises, which are critical in understanding dynamic phenomena such as price fluctuations and the spread of infectious…
This work aims at understanding the slow dynamics of a nonlocal fast-slow stochastic evolutionary system with stable Levy noise. Slow manifolds along with exponential tracking property for a nonlocal fast-slow stochastic evolutionary system…
This paper considers the problem of linear time-invariant (LTI) system identification using input/output data. Recent work has provided non-asymptotic results on partially observed LTI system identification using a single trajectory but is…
Recently, various models have been developed, including the fractional Brownian motion (fBm), to analyse the stochastic properties of geodetic time series, together with the extraction of geophysical signals. The noise spectrum of these…
This paper focuses on a stochastic system identification problem: given time series observations of a stochastic differential equation (SDE) driven by L\'{e}vy $\alpha$-stable noise, estimate the SDE's drift field. For $\alpha$ in the…
This paper addresses the problem of learning linear dynamical systems from noisy observations. In this setting, existing algorithms either yield biased parameter estimates or have large sample complexities. We resolve these issues by…