Related papers: Weak approximations for Wiener functionals
A general framework for the numerical approximation of evolution problems is presented that allows to preserve exactly an underlying Hamiltonian- or gradient structure. The approach relies on rewriting the evolution problem in a particular…
The non-Markovian nature of rough volatility processes makes Monte Carlo methods challenging and it is in fact a major challenge to develop fast and accurate simulation algorithms. We provide an efficient one for stochastic Volterra…
This paper provides convergence analysis for the approximation of a class of path-dependent functionals underlying a continuous stochastic process. In the first part, given a sequence of weak convergent processes, we provide a sufficient…
In this paper we analyze the approximation of stable linear time-invariant systems, like the Hilbert transform, by sampling series for bandlimited functions in the Paley-Wiener space $\mathcal{PW}_{\pi}^{1}$. It is known that there exist…
We introduce the local martingale problem associated to semilinear stochastic evolution equations driven by a cylindrical Wiener process and establish a one-to-one correspondence between solutions of the martingale problem and…
The rough Heston model is a very popular recent model in mathematical finance; however, the lack of Markov and semimartingale properties poses significant challenges in both theory and practice. A way to resolve this problem is to use…
We present a comprehensive discretization scheme for linear and nonlinear stochastic differential equations (SDEs) driven by either Brownian motions or $\alpha$-stable processes. Our approach utilizes compound Poisson particle…
We present a simple direct discretization for functionals used in the variational mesh generation and adaptation. Meshing functionals are discretized on simplicial meshes and the Jacobian matrix of the continuous coordinate transformation…
Malliavin Calculus is about Sobolev-type regularity of functionals on Wiener space, the main example being the Ito map obtained by solving stochastic differential equations. Rough path analysis is about strong regularity of solution to…
The paper develops a method for discrete computational Fourier analysis of functions defined on quasicrystals and other almost periodic sets. A key point is to build the analysis around the emerging theory of quasicrystals and diffraction…
We propose a straightforward and effective method for discretizing multi-dimensional diffusion processes as an extension of Milstein scheme. The new scheme is explicitly given and can be simulated using Gaussian variates, requiring the same…
We consider a finite element approximation of a general semi-linear stochastic partial differential equation (SPDE) driven by space-time multiplicative and additive noise. We examine the full weak convergence rate of the exponential Euler…
We study a class of fully-discrete schemes for the numerical approximation of solutions of stochastic Cahn--Hilliard equations with cubic nonlinearity and driven by additive noise. The spatial (resp. temporal) discretization is performed…
Problems of particle dynamics involving unsteady Stokes flows in confined geometries are typically harder to solve than their steady counterparts. Approximation techniques are often the only resort. Felderhof (see e.g. 2005, 2009b) has…
We consider a numerical scheme for Hamilton-Jacobi equations based on a direct discretization of the Lax-Oleinik semi-group. We prove that this method is convergent with respect to the time and space stepsizes provided the solution is…
We consider a method for the approximation of iterated stochastic integrals of arbitrary multiplicity $k$ $(k\in \mathbb{N})$ with respect to the infinite-dimensional $Q$-Wiener process using the mean-square approximation method of iterated…
In this contribution we derive and analyze a new numerical method for kinetic equations based on a variable transformation of the moment approximation. Classical minimum-entropy moment closures are a class of reduced models for kinetic…
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…
For a class of stochastic models with Gaussian and rough mean-reverting volatility that embeds the genuine rough Stein-Stein model, we study the weak approximation rate when using a Euler type scheme with integrated kernels. Our first…
This paper deals with the backward Euler method applied to semilinear parabolic stochastic partial differential equations (SPDEs) driven by additive noise. The SPDE is discretized in space by the finite element method and in time by the…