Related papers: Milstein schemes and antithetic multilevel Monte C…
Recently-proposed particle MCMC methods provide a flexible way of performing Bayesian inference for parameters governing stochastic kinetic models defined as Markov (jump) processes (MJPs). Each iteration of the scheme requires an estimate…
This paper is dedicated to investigating the adaptive Euler-Maruyama (EM) schemes for the approximation of McKean-Vlasov stochastic differential equations (SDEs) with common noise. When the drift and diffusion coefficients both satisfy the…
This paper concerns the nonparametric estimation problem of the distribution-state dependent drift vector field in an interacting $N$-particle system. Observing single-trajectory data for each particle, we derive the mean-field rate of…
We propose a new tamed Milstein-type scheme for stochastic differential equation with Markovian switching when drift coefficient is assumed to grow super-linearly. The strong rate of convergence is shown to be equal to $1.0$ under mild…
In this paper, we investigate gradient estimate of the Poisson equation and the exponential convergence in the Wasserstein metric $W_{1,d_{l^1}}$, uniform in the number of particles, and uniform-in-time propagation of chaos for the…
This paper deals with the Monte-Carlo methods for evaluating expectations of functionals of solutions to McKean-Vlasov Stochastic Differential Equations (MV-SDE) with drifts of super-linear growth. We assume that the MV-SDE is approximated…
We study large deviation properties of systems of weakly interacting particles modeled by It\^{o} stochastic differential equations (SDEs). It is known under certain conditions that the corresponding sequence of empirical measures…
In this article, we propose an implicit finite difference scheme for a two-dimensional parabolic stochastic partial differential equation (SPDE) of Zakai type. The scheme is based on a Milstein approximation to the stochastic integral and…
We present an abstract concept for the error analysis of numerical schemes for semilinear stochastic partial differential equations (SPDEs) and demonstrate its usefulness by proving the strong convergence of a Milstein-Galerkin finite…
Integration against a probability distribution given its unnormalized density is a central task in Bayesian inference and other fields. We introduce new methods for approximating such expectations with a small set of weighted samples --…
This paper focuses on two variants of the Milstein scheme, namely the split-step backward Milstein method and a newly proposed projected Milstein scheme, applied to stochastic differential equations which satisfy a global monotonicity…
We present an adaptive approximation scheme for jump-diffusion SDEs with discontinuous drift and (possibly) degenerate diffusion. This transformation-based doubly-adaptive quasi-Milstein scheme is the first scheme that has strong…
A first-order, Monte Carlo ensemble method has been recently introduced for solving parabolic equations with random coefficients in [26], which is a natural synthesis of the ensemble-based, Monte Carlo sampling algorithm and the…
We study McKean--Vlasov Stochastic Differential Equations (MV-SDEs) whose drift and diffusion coefficients are of superlinear growth in \textit{all} their variables thus also superlinear in the measure component (the meaning is specified in…
We use the linear scalar SDE as a test problem to show that it is possible to construct almost sure stable first-order weak balanced schemes based on the addition of stabilizing functions to the drift terms. Then, we design balanced schemes…
In this paper we consider Bayesian parameter inference associated to a class of partially observed stochastic differential equations (SDE) driven by jump processes. Such type of models can be routinely found in applications, of which we…
An explicit Milstein-type scheme for stochastic differential equation with Markovian switching is derived and its strong convergence in $\mathcal{L}^2$-sense is established without using It\^o-Taylor expansion formula. Rate of strong…
We study discrete-time simulation schemes for stochastic Volterra equations, namely the Euler and Milstein schemes, and the corresponding Multi-Level Monte-Carlo method. By using and adapting some results from Zhang [22], together with the…
In this paper, we study three numerical schemes for the McKean-Vlasov equation \[\begin{cases} \;dX_t=b(t, X_t, \mu_t) \, dt+\sigma(t, X_t, \mu_t) \, dB_t,\: \\ \;\forall\, t\in[0,T],\;\mu_t \text{ is the probability distribution of }X_t,…
In this paper a drift-randomized Milstein method is introduced for the numerical solution of non-autonomous stochastic differential equations with non-differentiable drift coefficient functions. Compared to standard Milstein-type methods we…