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We consider SDEs with bounded and $\alpha$-H\"older continuous drift, with $\alpha \in (0,1)$, driven by multiplicative noise. We show that under sufficient conditions on the diffusion matrix, which guarantee the existence of a unique…
This manuscript is dedicated to the numerical approximation of super-linear slow-fast stochastic differential equations (SFSDEs). Borrowing the heterogeneous multiscale idea, we propose an explicit multiscale Euler-Maruyama scheme suitable…
We study the strong rates of the Euler-Maruyama approximation for one dimensional stochastic differential equations whose drift coefficient may be neither continuous nor one-sided Lipschitz and diffusion coefficient is H\"older continuous.…
The numerical solutions of stochastic differential delay equations (SDDEs) under the generalized Khasminskii-type condition were discussed by Mao [15], and the theory there showed that the Euler-Maruyama (EM) numerical solutions converge to…
Time discretization along with space discretization is important in the numerical simulation of subsurface flow applications for long run. In this paper, we derive theoretical convergence error estimates in discrete-time setting for…
This paper is concerned with the numerical approximation of stochastic ordinary differential equations, which satisfy a global monotonicity condition. This condition includes several equations with super-linearly growing drift and diffusion…
We propose two Euler-Maruyama (EM) type numerical schemes in order to approximate the invariant measure of a stochastic differential equation (SDE) driven by an $\alpha$-stable L\'evy process ($1<\alpha<2$): an approximation scheme with the…
Deconvolution is the important problem of estimating the distribution of a quantity of interest from a sample with additive measurement error. Nearly all methods in the literature are based on Fourier transformation because it is…
Discretization of continuous-time diffusion processes is a widely recognized method for sampling. However, it seems to be a considerable restriction when the potentials are often required to be smooth (gradient Lipschitz). This paper…
In this paper, we consider stochastic differential equations whose drift coefficient is superlinearly growing and piece-wise continuous, and whose diffusion coefficient is superlinearly growing and locally H\"older continuous. We first…
We give an introductory account of the recent hyperdensity functional theory for the equilibrium statistical mechanics of soft matter systems [F. Samm\"uller et al., Phys. Rev. Lett. 133, 098201 (2024); 10.1103/PhysRevLett.133.098201].…
The understanding of adaptive algorithms for SDEs is an open area where many issues related to both convergence and stability (long time behaviour) of algorithms are unresolved. This paper considers a very simple adaptive algorithm, based…
It is well known that the Euler method for a random ordinary differential equation $\mathrm{d}X_t/\mathrm{d}t = f(t, X_t, Y_t)$ driven by a stochastic process $\{Y_t\}_t$ with $\theta$-H\"older sample paths is estimated to be of strong…
We are interested in the time discretization of stochastic differential equations with additive d-dimensional Brownian noise and L q -- L $\rho$ drift coefficient when the condition d $\rho$ + 2 q < 1, under which Krylov and R{\"o}ckner…
We study the error between the exact solution and its Euler-Maruyama approximation in temporal-spatial H\"older-norms for L\'evy-driven stochastic differential equations.
This paper studies the numerical simulation of the solution to the McKean-Vlasov equation with common noise. We begin by discretizing the solution in time using the Euler scheme, followed by spatial discretization through the particle…
Discretization of continuous-time diffusion processes is a widely recognized method for sampling. However, the canonical Euler Maruyama discretization of the Langevin diffusion process, referred as Unadjusted Langevin Algorithm (ULA),…
In this paper, we examine the performance of randomised Euler-Maruyama (EM) method for additive time-inhomogeneous SDEs with an irregular drift driven by symmetric $\alpha$-table process, $\alpha\in (1,2)$. In particular, the drift is…
In this paper, the truncated Euler-Maruyama (EM) method is employed together with the Multi-level Monte Carlo (MLMC) method to approximate the expectations of functions of solutions to stochastic differential equations (SDEs). The…
We show that generalized spherical harmonics are well suited for representing the space and orientation molecular density in the resolution of the molecular density functional theory. We consider the common system made of a rigid solute of…