Related papers: Approximation and simulation of infinite-dimension…
We consider a class of linear integral operators with impulse responses varying regularly in time or space. These operators appear in a large number of applications ranging from signal/image processing to biology. Evaluating their action on…
We reconstruct the velocity field of incompressible flows given a finite set of measurements. For the spatial approximation, we introduce the Sparse Fourier divergence-free (SFdf) approximation based on a discrete $L^2$ projection. Within…
We study the weak convergence behaviour of the Leimkuhler--Matthews method, a non-Markovian Euler-type scheme with the same computational cost as the Euler scheme, for the approximation of the stationary distribution of a one-dimensional…
Obtaining reliable numerical simulations of turbulent fluids is a challenging problem in computational fluid mechanics. The Large Eddy Simulations (LES) models are efficient tools to approximate turbulent fluids and an important step in the…
This paper deals with the approximation of the weak solutions of the incompressible Navier Stokes Fourier system. In particular it extends the artificial compressibility method for the Leray weak solutions of the Navier Stokes equation,…
Control design for linear, time-invariant mechanical systems typically requires an accurate low-order approximation in the low frequency range. For example a series expansion of the transfer function around zero consisting of a mass,…
Self-similar processes are useful in modeling diverse phenomena that exhibit scaling properties. Operator scaling allows a different scale factor in each coordinate. This paper develops practical methods for modeling and simulating…
We develop and analyze a general class of Euler-type numerical schemes for Levy-driven McKean-Vlasov stochastic differential equations (SDEs), where the drift, diffusion and jump coefficients grow super-linearly in the state variable. These…
Solving Bayesian inference problems approximately with variational approaches can provide fast and accurate results. Capturing correlation within the approximation requires an explicit parametrization. This intrinsically limits this…
In many Bayesian inverse problems the goal is to recover a spatially varying random field. Such problems are often computationally challenging especially when the forward model is governed by complex partial differential equations (PDEs).…
In this paper, we provide strong $L_2$-rates of approximation of the integral-type functionals of Markov processes by integral sums. We improve the method developed in [2]. Under assumptions on the process formulated only in terms of its…
Sampling from various kinds of distributions is an issue of paramount importance in statistics since it is often the key ingredient for constructing estimators, test procedures or confidence intervals. In many situations, the exact sampling…
In the present paper we study selfdecomposability of random fields, as defined directly rather than in terms of finite-dimensional distributions. The main tools in our analysis are the master L\'evy measure and the associated L\'evy-It\^o…
In this paper, we investigate time-varying nonlinear time series regression for a broad class of locally stationary time series. First, we propose sieve nonparametric estimators for the time-varying regression functions that achieve uniform…
We establish several closed pricing formula for various path-independent payoffs, under an exponential L\'evy model driven by the Variance Gamma process. These formulas take the form of quickly convergent series and are obtained via tools…
Approximate Bayesian computation methods are useful for generative models with intractable likelihoods. These methods are however sensitive to the dimension of the parameter space, requiring exponentially increasing resources as this…
We study Bayesian inference methods for solving linear inverse problems, focusing on hierarchical formulations where the prior or the likelihood function depend on unspecified hyperparameters. In practice, these hyperparameters are often…
We study the discrepancy between the distribution of a vector-valued functional of i.i.d. random elements and that of a Gaussian vector. Our main contribution is an explicit bound on the convex distance between the two distributions,…
A new algorithm for the approximation and simulation of twofold iterated stochastic integrals together with the corresponding L\'{e}vy areas driven by a multidimensional Brownian motion is proposed. The algorithm is based on a truncated…
We construct an efficient integrator for stochastic differential systems driven by Levy processes. An efficient integrator is a strong approximation that is more accurate than the corresponding stochastic Taylor approximation, to all orders…