Persistence and exit times for some additive functionals of skew Bessel processes

Let X be some homogeneous additive functional of a skew Bessel process Y. In this note, we compute the asymptotics of the first passage time of X to some fixed level b, and study the position of Y when X exits a bounded interval [a, b]. As a by-product, we obtain the probability that X reaches the level b before the level a. Our results extend some previous works on additive functionals of Brownian motion by Isozaki and Kotani for the persistence problem, and by Lachal for the exit time problem

Measurement of Cannibalism Effects in buying experiments using Mixed Logit Models - The Example of a new Brand of the “Fruits of Lake Constance” Association -

One fundamental assumption of discrete choice regression is the assumption of independence of irrelevant alternatives (IIA). According to the IIA assumption no correlation is allowed between brands in buying experiments. As a consequence, in market simulations all remaining brands gain at the ratio of their starting market share if one brand is excluded from the simulation set. This often does not reflect the reality at the point-of-sale. Mixed-logit models offer the advantage that the IIA-assumption is completely relaxed. What is more, simulations based on mixed logit are able to model cannibalism effects. This paper applies mixed logit to buying behaviour research. A case study is presented where the introduction of a new apple brand at the German discounter “Penny” is simulated in a buying experiment.Mixed Logit Model; IIA-assumption; cannibalism effect; choice experiment; apples

A Theoretical Framework for Country-of-Origin-Research in the Food sector

The main advancement of the developed theoretical framework for Country-of-Origin (CO) research in this paper is the holistic consideration of CO in consumer choice that is missing in older works as for example made by ITTERSUM (2003) or JAFFE AND NEBENZAHL (2001). These and other researchers describe a lot of aspects of the CO effect separately and inde-pendent from each other without paying a lot attention to the interdependencies. Furthermore the offered model integrates new but important impact factors on the CO effect. The devel-oped theoretical framework has to be tested empirical and therefore call for future CO re-search in the food sector.Country-of-Origin, Food, Theoretical Model

Windings of the stable Kolmogorov process

We investigate the windings around the origin of the two-dimensional Markov process (X,L) having the stable L\'evy process L and its primitive X as coordinates, in the non-trivial case when |L| is not a subordinator. First, we show that these windings have an almost sure limit velocity, extending McKean's result [McK63] in the Brownian case. Second, we evaluate precisely the upper tails of the distribution of the half-winding times, connecting the results of our recent papers [CP14, PS14]

Piecewise Constant Martingales and Lazy Clocks

This paper discusses the possibility to find and construct \textit{piecewise constant martingales}, that is, martingales with piecewise constant sample paths evolving in a connected subset of $\mathbb{R}$. After a brief review of standard possible techniques, we propose a construction based on the sampling of latent martingales $\tilde{Z}$ with \textit{lazy clocks} $\theta$. These $\theta$ are time-change processes staying in arrears of the true time but that can synchronize at random times to the real clock. This specific choice makes the resulting time-changed process $Z_t=\tilde{Z}_{\theta_t}$ a martingale (called a \textit{lazy martingale}) without any assumptions on $\tilde{Z}$, and in most cases, the lazy clock $\theta$ is adapted to the filtration of the lazy martingale $Z$. This would not be the case if the stochastic clock $\theta$ could be ahead of the real clock, as typically the case using standard time-change processes. The proposed approach yields an easy way to construct analytically tractable lazy martingales evolving on (intervals of) $\mathbb{R}$.Comment: 17 pages, 8 figure

Hopping-resolved electron-phonon coupling in bilayer graphene

In this paper we investigate the electron-phonon coupling in bilayer graphene, as a paradigmatic case for multilayer graphenes where interlayer hoppings are relevant. Using a frozen-phonon approach within the context of Density Functional Theory (DFT) and using different optical phonon displacements we are able to evaluate quantitatively the electron-phonon coupling $\alpha_i$ associated with each hopping term $\gamma_i$. This analysis also reveals a simple scaling law between the hopping terms $\gamma_i$ and the electron-phonon coupling $\alpha_i$ which goes beyond the specific DFT technique employed.Comment: 10 pages, 10 fig

A stable Langevin model with diffusive-reflective boundary conditions

In this note, we consider the construction of a one-dimensional stable Langevin type process confined in the upper half-plane and submitted to reflective-diffusive boundary conditions whenever the particle position hits 0. We show that two main different regimes appear according to the values of the chosen parameters. We then use this study to construct the law of a (free) stable Langevin process conditioned to stay positive, thus extending earlier works on integrated Brownian motion. This construction further allows to obtain the exact asymptotics of the persistence probability of the integrated stable L{\'e}vy process. In addition, the paper is concluded by solving the associated trace problem in the symmetric case