Solvability of forward–backward stochastic di erential equations with nonsmooth coe cients is considered using the Four-Step Scheme and some approximation arguments. For the onedimensional case, the existence of an adapted solution is established for the equation which allows the di usion in the forward equation to be degenerate. As a byproduct, we obtain the existence of a viscosity solution t...

We design a general mathematical framework to analyze the properties of nearest neighbor balancing algorithms of the di€usion type. Within this framework we develop a new Optimal Polynomial Scheme (OPS) which we show to terminate within a ®nite number m of steps, where m only depends on the graph and not on the initial load distribution. We show that all existing di€usion load balancing algorit...

We study an in nite period incomplete information dynamic game of a nite number of agents adopting a new technology with pure information externalities. Each agent has private information about his idiosyncratic adoption cost, but share the same public information, released by early adopters, about the technology's eÆciency, which is common to all agents. We show that a unique symmetric pure st...

We motivate and analyze a reaction-advection-di usion model for the dynamics of a phytoplankton species. The reproductive rate of the phytoplankton is determined by the local light intensity. The light intensity decreases with depth due to absorption by water and phytoplankton. Phytoplankton is transported by turbulent di usion in a water column of given depth. Furthermore, it might be sinking ...

We design a general mathematical framework to analyze the properties of nearest neighbor balancing algorithms of the di usion type. Within this framework we develop a new optimal polynomial scheme (OPS) which we show to terminate within a nite number m of steps, where m only depends on the graph and not on the initial load distribution. We show that all existing di usion load balancing algorith...

We consider the process dYt = utdt + dWt; where u is a process not necessarily adapted to FY (the ...ltration generated by the process Y ) and W is a Brownian Motion. We obtain a general representation for the likelihood ratio of the law of the Y process relative to Brownian measure. This representation involves only one basic ...lter (expectation of u conditional on observed process Y ): This ...

A model for long range di usion reaction on population dynamics has been considered, and conditions for the existence and uniqueness of solutions to the model in L p;q norms has been obtained.

A recently developed theory of uid mixing is summarized here. It describes linear advection of a passive scalar by a random velocity eld. Asymptotic scaling laws are given, which are consistently derived from leading order results of primitive and renormalized perturbation theory in both the Eulerian and Lagrangian pictures. The theory has been veri ed by numerical simulation, for moderately la...

We study the large time behavior of solutions of the Cauchy problem for a fast di usion equation with a singular powerlike source. It is shown that the large time behavior is described by the similarity solution of related problem.

In the context of convection-di usion equation, we consider the use of open boundary conditions (also called radiation boundary conditons) in Block GaussSeidel algorithms. Theoretical results and numerical tests show that the convergence is thus accelerated.