8 problems

Stochastic numerical methods are compared by their strong and weak convergence orders, with the strong error measuring the pathwise or mean-square approximation error over long-tim…

Let the linear Vlasov equations considered in the paper be perturbed by additive, multiplicative Itô, multiplicative Stratonovich, or transport Wiener noise, and let the correspond…

Consider the stochastic Maxwell–Bloch system with $\sigma_1=\sigma_3=1$, the proposed explicit stochastic Poisson integrator, and a test function used to measure weak error. Weak c…

Consider the stochastic Maxwell–Bloch system and the proposed explicit stochastic Poisson integrator, with noise parameter $\sigma_1=0$. Strong convergence of order $1$ means that…

The proposed near exact Euler–Maruyama scheme (n-EEM) is designed for nonlinear stochastic differential equations, where classical Euler–Maruyama (EM), Girsanov-corrected technique…

Let $u(t_n)$ be the exact solution and $u^n$ the numerical solution at time steps $t_n$, with $\tau$ the time-step size, $N$ the final step, and let $\mathbb{P}_W$ denote the proba…

Let the BISS method be a numerical scheme for the Wright–Fisher model, and let the true solution be the exact solution of that model. The method is known to converge to the true so…

Extension conjecture. Combining the present analysis with suitable methods from the analysis of stochastic differential equations should provide extensions of the convergence resul…