Related papers: Nonparametric estimation for L\'evy processes from…

In this paper, we consider the estimation and inference of precision matrices of a rich class of locally stationary and nonlinear time series assuming that only one realization of the time series is observed. Using a Cholesky decomposition…

In many random search processes of interest in chemistry, biology or during rescue operations, an entity must find a specific target site before the latter becomes inactive, no longer available for reaction or lost. We present exact results…

Ordinary Differential Equations are widespread tools to model chemical, physical, biological process but they usually rely on parameters which are of critical importance in terms of dynamic and need to be estimated directly from the data.…

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…

We derive a criterium for the almost sure finiteness of perpetual integrals of \LL processes for a class of real functions including all continuous functions and for general one-dimensional L\'evy processes that drifts to plus infinity.…

In this paper, an alternative approximation to the innovation method is introduced for the parameter estimation of diffusion processes from partial and noisy observations. This is based on a convergent approximation to the first two…

We propose a new statistical observation scheme of diffusion processes named convolutional observation, where it is possible to deal with smoother observation than ordinary diffusion processes by considering convolution of diffusion…

Using complex analysis techniques we obtain precise asymptotic approximations for the kernels corresponding to the symmetric $\alpha$-stable processes and their fractional derivatives. We apply our method to general L\'evy processes whose…

This article investigates the least squares estimators (LSE) for the unknown parameters in stochastic differential equations (SDEs) that are affected by L\'evy noise, particularly when the sample paths are sparse. Specifically, given $n$…

By using absolutely continuous lower bounds of the L\'evy measure, explicit gradient estimates are derived for the semigroup of the corresponding L\'evy process with a linear drift. A derivative formula is presented for the conditional…

This paper deals with nonparametric maximum likelihood estimation for Gaussian locally stationary processes. Our nonparametric MLE is constructed by minimizing a frequency domain likelihood over a class of functions. The asymptotic behavior…

We consider the problem of discrete-time signal denoising, focusing on a specific family of non-linear convolution-type estimators. Each such estimator is associated with a time-invariant filter which is obtained adaptively, by solving a…

We introduce a general algorithm for the computation of the scale functions of a spectrally negative L\'evy process $X$, based on a natural weak approximation of $X$ via upwards skip-free continuous-time Markov chains with stationary…

We consider a stochastic process driven by a diffusion and jumps. We devise a technique, which is based on a discrete record of observations, for identifying the times when jumps larger than a suitably defined threshold occurred. The…

In this paper, we consider a nonlinear filtering model with observations driven by correlated Wiener processes and point processes. We first derive a Zakai equation whose solution is a unnormalized probability density function of the filter…

Estimates of densities of convolution semigroups of probability measures are given under specific assumptions on the corresponding L\'evy measure and the L\'evy--Khinchin exponent. The assumptions are satisfied, e.g., by tempered stable…

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…

We present a relatively simple and mostly elementary proof of the L\'evy--Khintchine formula for subordinators. The main idea is to study the Poisson process time-changed by the subordinator. The technical tools used are conditional…

Assuming that a threshold Ornstein-Uhlenbeck process is observed at discrete time instants, we propose generalized moment estimators to estimate the parameters. Our theoretical basis is the celebrated ergodic theorem. To use this theorem we…

We revisit an absolutely-continuous version of the stochastic control problem driven by a L\'evy process. A strategy must be absolutely continuous with respect to the Lebesgue measure and the running cost function is assumed to be convex.…