In this paper, we first prove the weak convergence for the Moudafi’s iterative scheme of two quasi-nonexpansive mappings. Then we prove the weak convergence for the Moudafi’s iterative scheme of quasi-nonexpansive mapping and nonexpansive mapping. Finally, we prove the strong convergence for the Moudafi’s iterative scheme of two quasi-nonexpansive mappings. Our results generalize the recent res...

The stochastic heat equation driven by additive noise is discretized in the spatial variables by a standard finite element method. The weak convergence of the approximate solution is investigated and the rate of weak convergence is found to be twice that of strong convergence.

2 Two-Scale Convergence Definition and Results 15 2.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2 Link with Weak Convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.3 Injection Lemma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.4 Two-Scale Convergence criterion . . . . . . . . . . . . . . . . . . ....

We deene an Euler type weak approximation for solutions of nonlinear diiusion processes. We nd the rate of convergence of this scheme in weak form. As in the diiusion case the weak rate of convergence is better than the strong one. The proof uses the integration by parts formula of Malliavin calculus.

In this paper, we study the problem concerning stability and asymptotic behaviours of solutions for a degenerate Landau-Lifshitz equation in micromagnetics involving only the nonlocal magnetostatic energy. Due to the lack of derivative estimates, we do not have the compactness needed for strong convergence and the natural convergence is weak* convergence. By formulating the problem in a new fra...

In this article, we obtain the weak and strong rates of convergence of time integrals of non-smooth functions of a one dimensional diffusion process. We propose the use the exact simulation scheme to simulate the process at discretization points. In particular, we also present the rates of convergence for the weak and strong error of approximation for the local time of a one dimensional diffusi...