Generating stochastic trajectories with global dynamical constraints

We propose a method to exactly generate Brownian paths x c (t) that are constrained to return to the origin at some future time t f , with a given fixed area A f = ∫ 0 t f d t x c ( t ) under their trajectory. We derive an exact effective Langevin equation with an effective force that accounts for the constraint. In addition, we develop the corresponding approach for discrete-time random walks, with arbitrary jump distributions including Lévy flights, for which we obtain an effective jump distribution that encodes the constraint. Finally, we generalise our method to other types of dynamical constraints such as a fixed occupation time on the positive axis T f = ∫ 0 t f d t Θ x c ( t ) or a fixed generalised quadratic area A f = ∫ 0 t f d t x c 2 ( t ) .

Estimation of Genetic Parameters for Feeding Pattern Traits and Its Relationship to Feed Efficiency and Production Traits in Duroc Pigs

This study was conducted to estimate the genetic parameters of different feeding pattern traits, including average daily feed intake (ADFI), average occupation time per day (AOTD), average occupation time per visit (AOTV), average daily feeding rate (ADFR), average feeding rate per feeding visit (AFRV), average feed intake per feeding visit (AFIV), and average number of visits per day (ANVD), and their genetic relationship to production traits, such as on-test average daily gain (ADG), backfat thickness (BFT), loin muscle area (LMA), lean percentage (LP), and feed efficiency traits, such as feed conversion ratio (FCR) and five measures of residual feed intake (RFI1 to RFI5), in Duroc pigs (DD). The non-heritable common spatial pen effect was also estimated in all studied traits. The feeding pattern traits used in this study were derived from filtered feeding visits of 602 DD pigs. Using three animal models and the REML method, the genetic parameters revealed low to moderate heritability for ADFI (0.19 to 0.32) and AFIV (0.18 to 0.33), moderate heritability for ANVD (0.28 to 0.35) and AOTV (0.21 to 0.31), and high heritability for AOTD (0.73), ADFR (0.62 to 0.64), and AFRV (0.59 to 0.63). The addition of a common spatial pen effect in models 2 and 3 had a substantial impact, ranging from 8% to 23%, on the total variability of most feeding pattern traits, with the exception of AOTD, which only had a percentage variance of 0.30% due to the pen effect. The genetic and phenotypic correlation revealed that ADFI had consistent moderate to high genetic and phenotypic correlation with production and feed efficiency (FE) traits. However, selection against ADFI would negatively affect on-test ADG. Interestingly, the AOTD had no genetic correlation with ADG (0.04), low to moderate positive genetic correlation with FCR (0.27) and all RFI measures (0.24 to 0.33), and moderate negative correlation with LP (−0.39), indicating that selection for DD pigs with lower AOTD would not influence on-test ADG but may increase LP and improve feed efficiency by lowering FCR and all RFI measures. However, the corresponding phenotypic correlation of AOTD with production and feed efficiency traits was mostly weak, which can be attributed to the low residual or environmental correlation between these correlated traits. At the genetic level, the feeding pattern traits showed potential in improving feed efficiency and production traits. However, further studies are needed to evaluate their impact at phenotypic level.

Alpine relief limited by glacial occupation time

Glaciers exert a major control on the shape of mountain topography. They tend to reduce relief above and scour troughs below the equilibrium line altitude (ELA). While many studies report this dichotomy, relief-limiting effects are controversial due to difficulties in quantifying key factors such as the initial topography, the timing of glacial occupancy, or rock uplift counteracting glacial erosion. Consequently, effectivity and degree of glacial erosion remain ambiguous. In geologically and climatically well-investigated parts of the European Central Alps, our calculation of glacial occupation time (GOT) from Quaternary ELA variations allows the quantification of gradual topographic modifications generated by the cumulative impact of cirque erosion over the Quaternary. We show that under low uplift, relief is effectively limited by glacial and periglacial headwall retreat, leading to a decline in topographic relief as GOT increases. Conversely, higher uplift rates seem to induce more persistent valley glaciation, triggering a positive feedback loop in which steep slopes are protected against erosion and relief increases.

Supplemental Material: Alpine relief limited by glacial occupation time

Mean elevation, relief, and glacial occupation time (GOT) for delineated basins and 10 km² squares.<br>

Supplemental Material: Alpine relief limited by glacial occupation time

Mean elevation, relief, and glacial occupation time (GOT) for delineated basins and 10 km² squares.<br>

Occupation times of Lévy processes

In this paper, we give a complete and succinct proof that an explicit formula for the occupation time holds for all Lévy processes, which is important to the pricing problems of various occupation-time-related derivatives such as step options and corridor options. We construct a sequence of Lévy processes converging to a given Lévy process to obtain our conclusion. Besides financial applications, the mathematical results about occupation times of a Lévy process are of interest in applied probability.