Related papers: M-Estimation based on quasi-processes from discret…
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…
Monte Carlo and Quasi-Monte Carlo methods present a convenient approach for approximating the expected value of a random variable. Algorithms exist to adaptively sample the random variable until a user defined absolute error tolerance is…
We develop generic and efficient importance sampling estimators for Monte Carlo evaluation of prices of single- and multi-asset European and path-dependent options in asset price models driven by L\'evy processes, extending earlier works…
The aim of this paper is to develop estimation and inference methods for the drift parameters of multivariate L\'evy-driven continuous-time autoregressive processes of order $p\in\mathbb{N}$. Starting from a continuous-time observation of…
We study a Monte Carlo algorithm for simulation of probability distributions based on stochastic step functions, and compare to the traditional Metropolis/Hastings method. Unlike the latter, the step function algorithm can produce an…
Models of stochastic processes are widely used in almost all fields of science. Theory validation, parameter estimation, and prediction all require model calibration and statistical inference using data. However, data are almost always…
In this paper we discuss the possibility of using multilevel Monte Carlo (MLMC) methods for weak approximation schemes. It turns out that by means of a simple coupling between consecutive time discretisation levels, one can achieve the same…
In this article we consider likelihood-based estimation of static parameters for a class of partially observed McKean-Vlasov (POMV) diffusion process with discrete-time observations over a fixed time interval. In particular, using the…
Existing results for the estimation of the L\'evy measure are mostly limited to the onedimensional setting. We apply the spectral method to multidimensional L\'evy processes in order to construct a nonparametric estimator for the…
We consider quasi maximum likelihood (QML) estimation for general non-Gaussian discrete-ime linear state space models and equidistantly observed multivariate L\'evy-driven continuoustime autoregressive moving average (MCARMA) processes. In…
We consider a new method of the semiparametric statistical estimation for the continuous-time moving average L\'evy processes. We derive the convergence rates of the proposed estimators, and show that these rates are optimal in the minimax…
We consider the problem of static Bayesian inference for partially observed Levy-process models. We develop a methodology which allows one to infer static parameters and some states of the process, without a bias from the…
This work introduces a novel multilevel Monte Carlo (MLMC) metamodeling approach for variance function estimation. Although devising an efficient experimental design for simulation metamodeling can be elusive, the MLMC-based approach…
Irregular functional data in which densely sampled curves are observed over different ranges pose a challenge for modeling and inference, and sensitivity to outlier curves is a concern in applications. Motivated by applications in…
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 propose Subsampling MCMC, a Markov Chain Monte Carlo (MCMC) framework where the likelihood function for $n$ observations is estimated from a random subset of $m$ observations. We introduce a highly efficient unbiased estimator of the…
An important family of stochastic processes arising in many areas of applied probability is the class of L\'evy processes. Generally, such processes are not simulatable especially for those with infinite activity. In practice, it is common…
Quasi-Monte Carlo methods have proven to be effective extensions of traditional Monte Carlo methods in, amongst others, problems of quadrature and the sample path simulation of stochastic differential equations. By replacing the random…
In Kuznetsov et al. (2011) a new Monte Carlo simulation technique was introduced for a large family of Levy processes that is based on the Wiener-Hopf decomposition. We pursue this idea further by combining their technique with the recently…
The paper develops new methods of non-parametric estimation a compound Poisson distribution. Such a problem arise, in particular, in the inference of a Levy process recorded at equidistant time intervals. Our key estimator is based on…