Related papers: Calibration for multivariate L\'evy-driven Ornstei…
Inverse statistical physics aims at inferring models compatible with a set of empirical averages estimated from a high-dimensional dataset of independently distributed equilibrium configurations of a given system. However, in several…
A Thorin process is a stochastic process with independent and stationary increments whose laws are weak limits of finite convolutions of gamma distributions. Many popular L\'evy processes fall under this class. The Thorin class can be…
Bayesian inference provides a principled way of estimating the parameters of a stochastic process that is observed discretely in time. The overdamped Brownian motion of a particle confined in an optical trap is generally modelled by the…
We suppose that a L\'evy process is observed at discrete time points. Starting from an asymptotically minimax family of estimators for the continuous part of the L\'evy Khinchine characteristics, i.e., the covariance, we derive a…
We present a Bayesian framework based on a new exponential likelihood function driven by the quadratic Wasserstien metric. Compared to conventional Bayesian models based on Gaussian likelihood functions driven by the least-squares norm…
In this article we consider the Levy processes and the corresponding semigroup. We represent the generator of this semigroup in a convolution form. Using the obtained convolution form and the theory of integral equations we investigate the…
Flexible Bayesian models are typically constructed using limits of large parametric models with a multitude of parameters that are often uninterpretable. In this article, we offer a novel alternative by constructing an exponentially tilted…
We consider a sequence of fractional Ornstein-Uhlenbeck processes, that are defined as solutions of a family of stochastic Volterra equations with kernel given by the Riesz derivative kernel, and leading coefficients given by a sequence of…
We establish a general theory of optimal strong error estimation for numerical approximations of a second-order parabolic stochastic partial differential equation with monotone drift driven by a multiplicative infinite-dimensional Wiener…
We analyze confining mechanisms for L\'{e}vy flights. When they evolve in suitable external potentials their variance may exist and show signatures of a superdiffusive transport. Two classes of stochastic jump - type processes are…
The last decade has seen max-stable processes emerge as a common tool for the statistical modeling of spatial extremes. However, their application is complicated due to the unavailability of the multivariate density function, and so…
Using a coupling for the weighted sum of independent random variables and the explicit expression of the transition semigroup of Ornstein-Uhlenbeck processes driven by compound Poisson processes, we establish the existence of a successful…
The functional method to derive the fractional Fokker-Planck equation for probability distribution from the Langevin equation with Levy stable noise is proposed. For the Cauchy stable noise we obtain the exact stationary probability density…
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 prove a version of the Feynman-Kac formula for Levy processes and integro-differential operators, with application to the momentum representation of suitable quantum (Euclidean) systems whose Hamiltonians involve L\'{e}vy-type…
In this article, we study the problem of parameter estimation for a discrete Ornstein - Uhlenbeck model driven by Poisson fractional noise. Based on random walk approximation for the noise, we study least squares and maximum likelihood…
The Marshall-Olkin (MO) distribution has been considered a key model in reliability theory and in risk analysis, where it is used to model the lifetimes of dependent components or entities of a system and dependency is induced by "shocks"…
A spectral representation for regularly varying L\'evy processes with index between one and two is established and the properties of the resulting random noise are discussed in detail giving also new insight in the $L^2$-case where the…
In this paper we consider the existence of weakly c\`adl\`ag versions of a solution to a linear equation in a Hilbert space $H$, driven by a Levy process taking values in a Hilbert space $U$. In particular we are interested in diagonal type…
Modern methods of generative modelling and unpaired data translation based on Schr\"odinger bridges and stochastic optimal control theory aim to transform an initial density to a target one in an optimal way. In the present paper, we assume…