Yingyi Liu 1,*, Ying Gou 2, Bin Teng 2 and Shigeo Yoshida 1 1 Renewable Energy Center, Research Institute for Applied Mechanics, Kyushu University, Kasuga 8168580, Japan; [email protected] 2 State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China; [email protected] (Y.G.); [email protected] (B.T.) * Correspondence: liuyingyi@r...

where η is a N(0, 1) random variable independent of B and L denotes the convergence in law. This result has been first proved in [3] by using the method of moments. In [4] we gave a simple proof based on Clark-Ocone formula and an asymptotic version of Knight’s theorem (see Revuz and Yor [9], Theorem (2.3), page 524). Another simple proof of this result with the techniques of stochastic analysi...

We study convergence of a boundary integral method for 3D interfacial flow with surface tension when the fluid velocity is given by Darcy’s Law. The method is closely related to a previous method developed and implemented by Ambrose, Siegel, and Tlupova, in which one of the main ideas is the use of an isothermal parameterization of the free surface. We prove convergence by proving consistency a...