Related papers: Two-step estimation of a multivariate L\'evy proce…
We propose stepwise variational inference (VI) with vine copulas: a universal VI procedure that combines vine copulas with a novel stepwise estimation procedure of the variational parameters. Vine copulas consist of a nested sequence of…
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…
We develop a new model selection method for the adaptive robust efficient nonparametric signal estimation observed with impulse noise which is defined by the general non Gaussian L\'evy processes. On the basis of the developed method, we…
The article develops marginal models for multivariate longitudinal responses. Overall, the model consists of five regression submodels, one for the mean and four for the covariance matrix, with the latter resulting by considering various…
In this paper, we study the L\'evy process time-changed by independent L\'evy subordinators, namely, the incomplete gamma subordinator, the $\epsilon$-jumps incomplete gamma subordinator and tempered incomplete gamma subordinator. We derive…
In this paper we address the problem of rare-event simulation for heavy-tailed L\'evy processes with infinite activities. We propose a strongly efficient importance sampling algorithm that builds upon the sample path large deviations for…
This paper analyzes the limit properties of the empirical process of $\alpha$-stable random variables with long range dependence. The $\alpha$-stable random variables are constructed by non-linear transformations of bivariate sequences of…
Given a discrete time sample $X_1,... X_n$ from a L\'evy process $X=(X_t)_{t\geq 0}$ of a finite jump activity, we study the problem of nonparametric estimation of the characteristic triplet $(\gamma,\sigma^2,\rho)$ corresponding to the…
This paper addresses the estimation problem of an unknown drift parameter matrix for a fractional Ornstein-Uhlenbeck process in a multi-dimensional setting. To tackle this problem, we propose a novel approach based on rough path theory that…
This paper provides rate-efficient estimators of the volatility parameter in the presence of L\'{e}vy jumps
Several researchers have described two-part models with patient-specific stochastic processes for analysing longitudinal semicontinuous data. In theory, such models can offer greater flexibility than the standard two-part model with…
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…
We identify general conditions under which regenerative processes with dependent cycles and cycle lengths are asymptotically independent. The result is applied to various models. In particular, independent L\'evy processes with dependent…
Process convolutions yield random fields with flexible marginal distributions and dependence beyond Gaussianity, but statistical inference is often hampered by a lack of closed-form marginal distributions, and simulation-based inference may…
The goal of this paper is to investigate how the marginal and dependence structures of a variety of multivariate L\'evy models affect calibration and pricing. To this aim, we study the approaches of Luciano and Semeraro (2010) and Ballotta…
Interest in continuous-time processes has increased rapidly in recent years, largely because of high-frequency data available in many applications. We develop a method for estimating the kernel function $g$ of a second-order stationary…
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…
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…
We apply multilevel Monte Carlo for option pricing problems using exponential L\'{e}vy models with a uniform timestep discretisation to monitor the running maximum required for lookback and barrier options. The numerical results demonstrate…
We establish distributional limit theorems for the shape statistics of a concave majorant (i.e. the fluctuations of its length, its supremum, the time it is attained and its value at $T$) of any L\'evy process on $[0,T]$ as $T\to\infty$.…