Abstract. In this paper, the solvability of a class of forward-backward stochastic di erential equations (SDEs for short) over an arbitrarily prescribed time duration is studied. We design a stochastic relaxed control problem, with both drift and di usion all being controlled, so that the solvability problem is converted to a problem of nding the nodal set of the viscosity solution to a certain...

A model is developed for the ow of a slightly compressible uid through a saturated inelastic porous medium. The initial-boundary-value problem is a system that consists of the di usion equation for the uid coupled to the momentum equation for the porous solid together with a constitutive law which includes a possibly hysteretic relation of elasto-visco-plastic type. The variational form of this...

In the Cramér-Lundberg model and its di usion approximation, it is a classical problem to nd the optimal dividend payment strategy that maximizes the expected value of the discounted dividend payments until ruin. One often raised disadvantage of this approach is the fact that such a strategy does not take the life time of the controlled process into account. In this paper we introduce a value f...

The classical Petrov-Galerkin approach to Black Box multigrid for nonsymmetric problems due to Dendy is combined with the recent factor-three-coarsening Black Box algorithm due to Dendy and Moulton, along with a powerful symmetric line Gauss-Seidel smoother, resulting in an e cient and robust multigrid solver. Focusing on the convectiondi usion operator, the algorithm is tested and shown to ach...

For a large class of irregular grid applications, the structure of the mesh changes from one phase of the computation to the next. Eventually, as the graph evolves, the adapted mesh has to be repartitioned to ensure good load balance. If this new graph is partitioned from scratch, it will lead to an excessive migration of data among processors. In this paper, we present two new schemes for comp...

Di¡usion tensor imaging studies in schizophrenia have demonstratedlowerdi¡usion anisotropy withinwhitematter thatprovides information about brain white matter integrity.We have examined whether whitematter is abnormal in ¢rst-episode schizophrenia by using di¡usion tensor imaging. Twenty-one schizophrenic patients and healthy controls underwent di¡usion tensor imaging scans that analyzed by usi...

The Yale stellar evolution code has been modi ed to include the combined e ects of di usion and rotational mixing on 1 H, 4 He and the trace elements 3 He, 6 Li, 7 Li, and 9 Be. The interaction between rotational mixing and di usion is studied by calculating a number of calibrated solar models. The rotational mixing inhibits the di usion in the outer parts of the models, leading to a decrease i...

This paper investigates the statistical relationship of the GARCH model and its di usion limit. Regarding the two types of models as two statistical experiments formed by discrete observations from the models, we study their asymptotic equivalence in terms of Le Cam's de ciency distance. To our surprise, we are able to show that the GARCH model and its di usion limit are asymptotically equivale...

The forward di¤usion equation for gene frequency dynamics is solved subject to the condition that the total probability is conserved at all times. This can lead to solutions developing singular spikes (Dirac delta functions) at the gene frequencies 0 and 1. When such spikes appear in solutions they signal gene loss or gene …xation, with the “weight”associated with the spikes corresponding to th...

The e ect of arti cial di usion on discrete shock structures is examined for a family of schemes which includes scalar di usion, convective upwind and split pressure (CUSP) schemes, and upwind schemes with characteristic splitting. The analysis leads to conditions on the di usive ux such that stationary discrete shocks can contain a single interior point. The simplest formulation which meets th...