Abstract. This paper investigates the position (state) distribution of the single step bi-nomial (multi-nomial) process on a discrete state / time grid under the assumption that the velocity process rather than the state process is Markovian. In this model the particle follows a simple multi-step process in velocity space which also preserves the proper state equation of motion. Many numerical numerical examples of this process are provided. For a smaller grid the probability construction converges into a correlated set of probabilities of hyperbolic functions for each velocity at each state point. It is shown that the two dimen-sional process can be transformed into a Telegraph equation and via transformation into a Klein-Gordon equation if the transition rates are constant. In the last Section there is an example of multi-dimensional hyperbolic partial differential equation whose numerical aver-age satisfies Newton’s equation. There is also a momentum measure provided both for the two-dimensional case as for the multi-dimensional rate matrix.

In this paper we establish a Harnack inequality for nonnegative harmonic functions of some discontinuous Markov processes with a diffusion part.

In this paper we consider two semimartingales driven by diffusions and jumps. We allow both for finite activity and for infinite activity jump components. Given discrete observations we disentangle the integrated covariation (the covariation between the two diffusion parts, indicated by IC) from

We prove regularity (i.e., smoothness) of measures on R d satisfying the equation L = 0 where L is an operator of type Lu = tr(Au 00 ) +B \Delta ru. Here A is a Lipschitz continuous, uniformly elliptic matrix-valued map and B is merely -square integrable. We also treat a class of corresponding infinite dimensional cases where IR d is replaced by a locally convex topological vector space X . In this cases is absolutely continuous w.r.t. a Gaussian measure on X and the square root of the Radon-Nikodym density belongs to the Malliavin test function space ID 2;1 .

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Abstract: Competition between rival brands within the same category gives rise to special competition/substitution effects of great interest for involved firms. In the companion article, we studied balanced models that are adequate to describe a homogeneous category for which within-brand and cross-brand word-of-mouth effects are indistinguishable. Conversely, in this paper we propose an unbalanced model that, besides separating these two imitative sources, also allows for a change in the parameter values of the first entrant as soon as the second one enters the market. We prove that our model has a closedform solution allowing parameters to be estimated with sales data. Moreover, we compare our model with other unbalanced models, both from a theoretical point of view and from an empirical one, by comparing their performance on pharmaceutical drug data.

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descriptions at different scales. The process of iterating or diffusing the Markov matrix is seen as a generalization of some aspects of the Newtonian paradigm, in which local infinitesimal transitions of a system lead to global macroscopic descriptions by integration. In Part I below, we provide a unified

ABSTRACT: Translational diffusion is the most fundamental form of transport in chemical and biochemical systems. Pulsed-field gradient nuclear magnetic resonance provides a convenient and noninvasive means for measuring translational motion. In this method the attenuation of the echo signal from a

of the penalty, but find little evidence of this beyond the tendency of more mothers to work part-time. The portion of the motherhood penalty we cannot explain probably results from effects of motherhood on productivity and/or from employers' discrimination against mothers. While the benefits of mothering