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.

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...

In this paper, we examine the cause of the border e ect observed in many mobility models used to construct simulations of ad hoc networking protocol performance. We specify conditions under which a node mobility model must produce spatial mobile node distribution functions that obey the di usion equation. In particular demonstrate that these conditions are satis ed by the random direction (RD) ...

The di usion orientation distribution function (ODF) can be reconstructed from q-ball imaging (QBI) to map the complex intravoxel structure of water di usion. As acquisition time is particularly large for high angular resolution di usion imaging (HARDI), fast estimation algorithms have recently been proposed, as an on-line feedback on the reconstruction accuracy. Thus the acquisition could be s...

This paper develops a Multivariate Weighted Nonlinear Least Square estimator for a jumpdi usion interest rate model (hereafter MWNLS-JD), which also admits a closed form solution to bond price under an equilibrium martingale pricing theorem. The instantaneous interest rate is modeled as a mixture of a continuous square-root di usion and a discrete Poisson jump process, with the jump sizes unifo...

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 ...

This work introduces a generalised hybridisation strategy which utilises the information sharing mechanism deployed in Stochastic Di usion Search when applied to a number of population-based algorithms, e ectively merging this nature-inspired algorithm with some population-based algorithms. The results reported herein demonstrate that the hybrid algorithm, exploiting information-sharing within ...

We derive a cell-centered 3-D di usion di erencing scheme for arbitrary hexahedral meshes using the local support-operators method. Our method is said to be local because it yields a sparse matrix representation for the di usion equation, whereas the traditional support-operators method yields a dense matrix representation. The di usion discretization scheme that we have developed o ers several...

We compare two load balancing techniques for Cayley graphs based on information and load exchange between neighboring vertices. In the rst scheme, called natural di usion, each vertex gives (or receives) a xed part of the load di erence to (from) its direct neighbors. In the second scheme, called Cayley di usion, each vertex successively gives (or receives) a part of the load di erence to (or f...