Mercè Farré

MULTIPLE STRATONOVICH INTEGRAL AND HU―MEYER FORMULA FOR LÉVY PROCESSES

In the framework of vector measures and the combinatorial approach to stochastic multiple integral introduced by Rota and Wallstrom [Ann. Probab. 25 (1997) 1257―1283], we present an Ito multiple integral and a Stratonovich multiple integral with respect to a Levy process with finite moments up to a convenient order. In such a framework, the Stratonovich multiple integral is an integral with respect to a product random measure whereas the Ito multiple integral corresponds to integrate with respect to a random measure that gives zero mass to the diagonal sets. A general Hu-Meyer formula that gives the relationship between both integrals is proved. As particular cases, the classical Hu-Meyer formulas for the Brownian motion and for the Poisson process are deduced. Furthermore, a pathwise interpretation for the multiple integrals with respect to a subordinator is given.

Orientation domains: A mobile grid clustering algorithm with spherical corrections

An algorithm has been designed and tested which was devised as a tool assisting the analysis of geological structures solely from orientation data. More specifically, the algorithm was intended for the analysis of geological structures that can be approached as planar and piecewise features, like many folded strata. Input orientation data is expressed as pairs of angles (azimuth and dip). The algorithm starts by considering the data in Cartesian coordinates. This is followed by a search for an initial clustering solution, which is achieved by comparing the results output from the systematic shift of a regular rigid grid over the data. This initial solution is optimal (achieves minimum square error) once the grid size and the shift increment are fixed. Finally, the algorithm corrects for the variable spread that is generally expected from the data type using a reshaped non-rigid grid. The algorithm is size-oriented, which implies the application of conditions over cluster size through all the process in contrast to density-oriented algorithms, also widely used when dealing with spatial data. Results are derived in few seconds and, when tested over synthetic examples, they were found to be consistent and reliable. This makes the algorithm a valuable alternative to the time-consuming traditional approaches available to geologists.

Hyperbolic stochastic differential equations: Absolute continuity of the LKW of the solution at a fixed point

AbstractLetW be the Wiener process onT=[0, 1]2. Consider the stochastic integral equation

Interspecific hybridization increases transposition rates of Osvaldo.

\begin{gathered} X_\zeta = x_0 + \int_{R_\zeta } {a_1 (\zeta \prime )X(s\prime ,dt\prime )ds\prime + } \int_{R_\zeta } {a_2 (\zeta \prime )X(ds\prime ,t\prime )dt\prime } \hfill \\ + \int_{R_\zeta } {a_3 (X_{\zeta \prime , } \zeta \prime )W(ds\prime ,dt\prime ) + } \int_{R_\zeta } {a_4 (X_{\zeta \prime , } \zeta \prime )ds\prime ,dt\prime ,} \hfill \\ \end{gathered}

Relating Diversity and Human Appropriation from Land Cover Data

whereRζ=(s, t) ∈ T, andx0 ∈ ℝ. Under some assumptions on the coefficients ai, the existence and uniqueness of a solution for this stochastic integral equation is already known (see [6]). In this paper we present some sufficient conditions for the law ofXζ to have a density.

Multiple Stratonovich integral and HuMeyer formula for Lvy processes

Abstract The aim of this observational study is to identify risk factors associated with body weight (BW) variability in three data sets (DS) in commercial conditions. A total of 1,009 (DS1), 460 (DS2), and 1304 (DS3) male and female crossbreed pigs (Pietrain × [Landrace × Large White]), respectively, were included in each trial. Pigs were periodically weighed until slaughter. Then, variables such as length of gestation, length of lactation, parity, litter size, sex, birth BW, and ADG were considered. Pigs remaining on the farm after two loads to the slaughterhouse were defined as last group of animals sent to slaughterhouse (LGS). Descriptive statistics of variability were calculated, and a risk analysis approach was used to look for the factors related to LGS. A multiple logistic regression was performed to identify all variables that were significant (P < 0.05). The risk ratio (RR), odds ratio (OR), and population attributable risk (PAR) were calculated for all of the significant variables after transforming all of them into binary factors using the 25th percentile as the cut-off point. Results showed that the major part of the variability (as CV) comes from birth (20% to 25%) and increased only a little during lactation and 14-d post weaning. From this point onwards, CV tended to decrease, as pigs got closer to the marketing weight (down 11.5% to 12.7%). Regarding the indicators selected, RR, OR, and PAR presented similar trends in the three DS studied. Therefore, for the variables finally included, these indicators had their minimum values at the start of the cycle and then gradually increased at the end. Those results, based on an epidemiological approach, suggest that the closer to the end of the cycle the greater the probability for a light piglet of being/becoming LGS. It might be explained by the shorter available time to efficiently implement preventive measures aimed to improve the performance of delayed pigs and, thus, reducing variability.Those results, based on an epidemiological approach, make sense as the probability for a light piglet to be a LGS increases the closer to the end of the cycle, due to the short time to implement preventive measures and increase the performance of delayed pigs and reduce variability. The differential PAR associated with both, the nursery and the growing period, was 1.7% and 1.5% for DS1, 5.1% and 3.1% for DS2, and 3.7% and 2.8% for DS3. For the lactation period, the results were 4.3% for DS2 and 4.5% for DS3. Results suggest that the most critical periods, in relation to retardation of growth in swine, are lactation and nursery. Implementing measures that maintain risk factors under or above thresholds, especially in the initial phases of growth, will reduce the percentage of LGS pigs and positively affect the overall homogeneity of the batch.