Diffusion hitting times and the Bell-shape

Consider a generalized diffusion on R with speed measure m, in the natural scale. It is known that the conditional hitting times have a unimodal density function. We show that these hitting densities are bell-shaped if and only if m has infinitely many points of increase between the starting point and the hit point. This result can be viewed as a visual corollary to Yamazato's general factorization for diffusion hitting times.Comment: To appea

The Social Construction of the Audit Expectation Gap: The Market of Excuses

Nous examinons dans cet article l'“audit expectation gap” en nous appuyant sur l'étude de l'évolution des objectifs de l'audit dans le contexte français. La méthode d'investigation repose sur 9 entretiens réalisés auprès de commissaires aux comptes et sur 162 articles publiés entre 1966 et 2007 dans 5 revues comptables professionnelles. L'étude longitudinale permet de donner une description de l'évolution de l'expectation gap durant la période 1966-2007. Nous estimons que l'“expectation gap” est une notion socialement construite permettant aux auditeurs de justifier et de conserver leur statut sur le marché. Nous concluons que ce concept sert d'excuse à la profession d'audit.audit, construction sociale de l' “expectation gap”, archives, marché des excuses

A Mathematical Approach to Order Book Modeling

Motivated by the desire to bridge the gap between the microscopic description of price formation (agent-based modeling) and the stochastic differential equations approach used classically to describe price evolution at macroscopic time scales, we present a mathematical study of the order book as a multidimensional continuous-time Markov chain and derive several mathematical results in the case of independent Poissonian arrival times. In particular, we show that the cancellation structure is an important factor ensuring the existence of a stationary distribution and the exponential convergence towards it. We also prove, by means of the functional central limit theorem (FCLT), that the rescaled-centered price process converges to a Brownian motion. We illustrate the analysis with numerical simulation and comparison against market data

Further examples of GGC and HCM densities

We display several examples of generalized gamma convoluted and hyperbolically completely monotone random variables related to positive $\alpha$-stable laws. We also obtain new factorizations for the latter, refining Kanter's and Pestana-Shanbhag-Sreehari's. These results give stronger credit to Bondesson's hypothesis that positive $\alpha$-stable densities are hyperbolically completely monotone whenever $\alpha\le1/2.$Comment: Published in at http://dx.doi.org/10.3150/12-BEJ431 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

On exponential functionals, harmonic potential measures and undershoots of subordinators

We establish a link between the distribution of an exponential functional I and the undershoots of a subordinator, which is given in terms of the associated harmonic potential measure. This allows us to give a necessary and sufficient condition in terms of the L\'evy measure for the exponential functional to be multiplicative infinitely divisible. We then provide a formula for the moment generating function of an exponential functional $I$ and the so called remainder random variable $R$ associated to it. We provide a realization of the remainder random variable $R$ as an infinite product involving independent last position random variables of the subordinator. Some properties of harmonic measures are obtained and some examples are provided.Comment: 24 page

Efficient haploid production on 'Wilking' mandarin by induced gynogenesis

Seedlessness is a major criterion for the citrus fresh fruit market. Therefore, triploid breeding appears very promising for the selection of new citrus cultivars. CIRAD has developed a method to produce triploid hybrids by somatic hybridization between diploid and haploid lines, and demonstrates the potential for haploid citrus production by induced gynogenesis in clementine. In this work we analysed the efficiency of induced gynogenesis by irradiated pollen in 'Wilking' mandarin (Citrus reticulata). Five doses of gamma irradiation of 'Meyer' lemon pollen were tested (0, 150, 200, 250, 300 Grays). Embryos were extracted from small seeds, obtained in immature fruits, and cultivated in vitro. The ploidy level of plantlets was determined by flow cytometry analysis. Irradiated pollen appeared to be efficient for gynogenesis induction in 'Wilking'. A relatively high number of haploids (7 plantlets) were obtained, essentially after hybridisation with 'Meyer' lemon pollen irradiated at 250 Grays. The ploidy level of all haploid plantlets was confirmed by chromosome counts, and molecular markers demonstrated their gynogenetic origin. These haploid lines should be useful for triploid breeding by somatic hybridisation, and also constitute interesting resources for genomic studies. (Résumé d'auteur