Related papers: Optimal simulation schemes for L\'evy driven stoch…
We study a discrete time approximation scheme for the solution of a doubly reflected Backward Stochastic Differential Equation (DBBSDE in short) with jumps, driven by a Brownian motion and an independent compensated Poisson process.…
We provide a unifying approximate dynamic programming framework that applies to a broad variety of problems involving sequential estimation. We consider first the construction of surrogate cost functions for the purposes of optimization,…
In this article we show a robustness theorem for controlled stochastic differential equations driven by approximations of Brownian motion. Often, Brownian motion is used as an idealized model of a diffusion where approximations such as…
In this article, we consider multilevel Monte Carlo for the numerical computation of expectations for stochastic differential equations driven by L\'{e}vy processes. The underlying numerical schemes are based on jump-adapted Euler schemes.…
Our subject of study is strong approximation of stochastic differential equations (SDEs) with respect to the supremum error criterion, and we seek approximations that are strongly asymptotically optimal in specific classes of…
This paper introduces a randomized tamed Euler scheme tailored for L\'evy-driven stochastic differential equations (SDEs) with superlinear random coefficients and Carath\'eodory-type drift. Under assumptions that allow for time-irregular…
We are concerned with the discretization of a solution of a Forward-Backward stochastic differential equation (FBSDE) with a jump process depending on the Brownian motion. In this paper, we study the cases of Lipschitz generators and the…
We consider the problem of finding a stopping time that minimises the $L^1$-distance to $\theta$, the time at which a L\'evy process attains its ultimate supremum. This problem was studied in [12] for a Brownian motion with drift and a…
In the present work, we establish the approximation of nonlinear stochastic partial differential equation (SPDE) driven by cylindrical {\alpha}-stable L\'evy processes via modulation or amplitude equations. We study SPDEs with a cubic…
We introduce and compare computational techniques for sharp extreme event probability estimates in stochastic differential equations with small additive Gaussian noise. In particular, we focus on strategies that are scalable, i.e. their…
The pricing of options in exponential Levy models amounts to the computation of expectations of functionals of Levy processes. In many situations, Monte-Carlo methods are used. However, the simulation of a Levy process with infinite Levy…
We investigate numerical approximations for the stochastic Burgers equation driven by an additive cylindrical fractional Brownian motion with Hurst parameter $H \in (\frac{1}{2}, 1)$. To discretize the continuous problem in space, a…
Probabilistic ordinary differential equation (ODE) solvers have been introduced over the past decade as uncertainty-aware numerical integrators. They typically proceed by assuming a functional prior to the ODE solution, which is then…
In a recent paper by Kamrani et al. (2024), exponential Euler method for stiff stochastic differential equations with additive fractional Brownian noise was discussed, and the convergence order close to the Hurst parameter H was proved.…
This paper deals with U-statistics of Poisson processes and multiple Wiener-It\^o integrals on the Poisson space. Via sharp bounds on the cumulants for both classes of random variables, moderate deviation principles, concentration…
Models incorporating uncertain inputs, such as random forces or material parameters, have been of increasing interest in PDE-constrained optimization. In this paper, we focus on the efficient numerical minimization of a convex and smooth…
In this paper, we consider parameter estimation for stochastic differential equations driven by Wiener processes and compound Poisson processes. We assume unknown parameters corresponding to coefficients of the drift term, diffusion term,…
In this paper we present a weak approximation scheme for BSDEs driven by a Wiener process and an (in)finite activity Poisson random measure with drivers that are general Lipschitz functionals of the solution of the BSDE. The approximating…
We construct a nonstandard finite difference numerical scheme to approximate stochastic differential equations (SDEs) using the idea of weighed step introduced by R.E. Mickens. We prove the strong convergence of our scheme under locally…
In recent years, interest in approximation methods for stochastic differential equations (SDEs) with non-Lipschitz continuous coefficients has increased. We show lower bounds for the $L^p$-error of such methods in the case of approximation…