We analyse the strong approximation of the Cox–Ingersoll–Ross (CIR) process in the
regime where the process does not hit zero by a positivity preserving drift-implicit Euler-type …

We develop a perturbation theory for stochastic differential equations (SDEs) by which we
mean both stochastic ordinary differential equations (SODEs) and stochastic partial …

We consider the problem of sampling from constrained distributions, which has posed
significant challenges to both non-asymptotic analysis and algorithmic design. We propose …

The goal of this paper is to approximate two kinds of McKean–Vlasov stochastic differential
equations (SDEs) with irregular coefficients via weakly interacting particle systems. More …

Developed from the author's course at the Ecole Polytechnique, Monte-Carlo Methods and
Stochastic Processes: From Linear to Non-Linear focuses on the simulation of stochastic …

The celebrated Hörmander condition is a sufficient (and nearly necessary) condition for a
second-order linear Kolmogorov partial differential equation (PDE) with smooth coefficients …

We consider the Euler-Maruyama approximation for multi-dimen-sional stochastic
differential equations with irregular coefficients. We provide the rate of strong convergence …

We prove strong convergence of order 1/4-ϵ 1/4-ϵ for arbitrarily small ϵ> 0 ϵ> 0 of the Euler–
Maruyama method for multidimensional stochastic differential equations (SDEs) with …

We consider the approximation of one-dimensional stochastic differential equations (SDEs)
with non-Lipschitz drift or diffusion coefficients. We present a modified explicit Euler …

In this paper, we are concerned with convergence rate of Euler–Maruyama scheme for
stochastic differential equations with Hölder–Dini continuous drifts. The key contributions are …