We consider the weak convergence of numerical methods for stochastic differential equations (SDEs). Weak convergence is usually expressed in terms of the convergence of expected values of test functions of the trajectories. Here we present an alternative formulation of weak convergence in terms of the well-known Prokhorov metric on spaces of random variables. For a general class of methods, we ...

A classic ‘reference’ variable provides an indirect way to access a variable or aggregate. packetC, [1] a language for network packet processing, has specialized requirements for references that apply to aggregates, based on domain-specific, extended data types. The primary functional requirement is to defer selecting particular aggregates until runtime. In addition, requirements for high progr...

This paper presents novel and efficient strategies to spatially adapt the amount of computational effort applied based on the local dynamics of a free surface flow, for classic weakly compressible SPH (WCSPH). Using a convenient and readily parallelizable block-based approach, different regions of the fluid are assigned differing time steps and solved at different rates to minimize computationa...

We examine the problem of how to ensure behavioral consistency of an object-oriented system after its schema has been updated. The problem is viewed from the perspective of both the strongly typed and the untyped language model. Solutions are compared in both models using C++ and CLOS as examples.

A criterion is given for a strong type in a finite rank stable theory T to be (almost) internal to a given nonmodular minimal type. The motivation comes from results of Campana which give criteria for a compact complex analytic space to be “algebraic” (namely Moishezon). The canonical base property for a stable theory states that the type of the canonical base of a stationary type over a realis...

Two areas where common object-oriented modeling power lacks the necessary expressiveness are identi ed. An analysis of the situation shows that there exists a single reason why the real world situations cannot be modeled adequately. What really is missing is a means to express that objects of a certain type are able to behave in a fashion objects of another type would do. To remedy this situati...