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...

in this paper, we propose an algorithm for numerical solving an inverse non-linear diusion problem. in additional, the least-squares method is adopted tond the solution. to regularize the resultant ill-conditioned linear system ofequations, we apply the tikhonov regularization method to obtain the stablenumerical approximation to the solution. some numerical experiments con-rm the utility of...

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...

The transient drift di usion model describing the charge transport in semiconductors is con sidered Poisson s equation which is usually used is replaced by Maxwell s equations The di usion and mobility coe cients and the dielectric and magnetic susceptibilities may depend on the space variables Global existence and convergence to the thermal equilibrium is shown

This paper studies the problem of di usion in Markovian models such as hidden Markov models HMMs and how it makes very di cult the task of learning of long termdependencies in sequences Using results from Markov chain theory we show that the problem of di usion is reduced if the transition probabilities approach or Under this condition standard HMMs have very limited modeling capabilities but i...

In this paper we consider N−phased investment opportunities where the time evolution of the project value follows a jump-di usion process. An explicit valuation formula is derived under two di erent scenarios: in the rst case we consider xed and certain investment costs and in the second case we consider cost uncertainty and assume that investment costs follow a jump-di usion process.

A ®rm's ability to compete in new product markets is vital to its pro®tability and long-term survival. Therefore, it is important to understand the development and growth of these markets. Following a pioneering study by Bass (1969), di€usion models have traditionally provided this understanding in marketing. The great appeal of the Bass model is that it is a simple one that ®ts the data very w...

In this paper we investigate a family of partial di erential equations (PDEs) for image processing which can be regarded as isotropic nonlinear di usion with an additional factor on the right-hand side. The one-dimensional analogues to this lter class have been motivated as scaling limits of one-dimensional adaptive averaging schemes. In 2-D, mean curvature motion is one of the most prominent e...

We consider a nonstationary Markov multiserver queueing model where waiting customers may abandon and subsequently retry. In this paper we derive uid and di usion approximations for the associated waiting time process. The uid and di usion approximations for the corresponding queue length process were obtained in [4] (see also [5]).