The deterministic Skorohod problem plays an important role in the construction and analysis of diffusion processes with reflection. In the form studied here, the multidimensional Skorohod problem was introduced, in time-independent domains, by H. Tanaka [61] and further investigated by P.-L. Lions and A.-S. Sznitman [42] in their celebrated article. Subsequent results of several researchers have resulted in a large literature on the Skorohod problem in time-independent domains. In this article we conduct a thorough study of the multidimensional Skorohod problem in time-dependent domains. In particular, we prove the existence of c\`{a}dl\`{a}g solutions $(x,\lambda)$ to the Skorohod problem, with oblique reflection, for $(D,\Gamma,w)$ assuming, in particular, that $D$ is a time-dependent domain (Theorem 1.2). In addition, we prove that if $w$ is continuous, then $x$ is continuous as well (Theorem 1.3). Subsequently, we use the established existence results to construct solutions to stochastic differential equations with oblique reflection (Theorem 1.9) in time-dependent domains. In the process of proving these results we establish a number of estimates for solutions to the Skorohod problem with bounded jumps and, in addition, several results concerning the convergence of sequences of solutions to Skorohod problems in the setting of time-dependent domains.Comment: Published in at http://dx.doi.org/10.1214/10-AOP538 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org
A generalized linear model based on Poisson regression has been used to assess the impact of environmental variables modulating tropical cyclone frequency in six main cyclone development areas: the East Pacific, West Pacific, North Atlantic, North Indian, South Indian, and South Pacific. The analysis covers the period 1980–2009 and focuses on widely used meteorological parameters including wind shear, sea surface temperature, and relative humidity from different reanalyses as well as aerosol optical depth for different compounds simulated by the Goddard Chemistry Aerosol Radiation and Transport model. Circulation indices are also included. Cyclone frequency is obtained from the International Best Track Archive for Climate Stewardship. A strong link is found between cyclone frequency and the relative sea surface temperature, Atlantic Meridional Mode, and wind shear with significant explained log likelihoods in the North Atlantic of 37%, 27%, and 28%, respectively. A significant impact of black carbon and organic aerosols on cyclone frequency is found over the North Indian Ocean, with explained log likelihoods of 27%. A weaker but still significant impact is found for observed dust aerosols in the North Atlantic with an explained log likelihood of 11%. Changes in lower stratospheric temperatures explain 28% of the log likelihood in the North Atlantic. Lower stratospheric temperatures from a subset of Coupled Model Intercomparison Project Phase 5 models properly simulate the warming and subsequent cooling of the lower stratosphere that follows a volcanic eruption but underestimates the cooling by about 0.5°C.
Many microbial pathogens invade and proliferate within host cells and the molecular mechanism underlying this behavior is currently being revealed for several bacterial species. Testing clinically relevant antibacterial compounds and elucidating their effects on gene expression requires adequate controls, especially when studying genetically intractable organisms such as Chlamydia spp., for which various gene fusions cannot be constructed. Until now, relative mRNA levels in Chlamydia have been measured using different internal gene expression controls, including 16S rRNA, mRNAs, and DNA. Here, we compared the advantages and disadvantages of various internal expression controls during the early phase of Chlamydia pneumoniae development. The relative abundance of target mRNAs varied using the different internal control RNAs. This was partly due to variation in the transcript stability of the RNA species. Also, seven out of nine of the analyzed RNAs increased fivefold or more between 2 and 14 h postinfection, while the amount of DNA and number of cells remained essentially unaltered. Our results suggest that RNA should not be used as a gene expression control during the early phase of Chlamydia development, and that intrinsic bacterial DNA is preferable for that purpose because it is stable, abundant, and its relative amount is generally correlated with bacterial numbers.
In this article, we consider non-smooth time-dependent domains whose boundary is W 1,p in time and single-valued, smoothly varying directions of reflection at the boundary. In this setting, we first prove existence and uniqueness of strong solutions to stochastic differential equations with oblique reflection. Secondly, we prove, using the theory of viscosity solutions, a comparison principle for fully nonlinear second-order parabolic partial differential equations with oblique derivative boundary conditions. As a consequence, we obtain uniqueness, and, by barrier construction and Perron's method, we also conclude existence of viscosity solutions. Our results generalize two articles by Dupuis and Ishii to time-dependent domains.2000 Mathematics Subject Classification. 35D05, 49L25, 60J50, 60J60.
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