Stochastic delay equations with non-negativity constraints driven by fractional Brownian motion

In this note we prove an existence and uniqueness result for the solution of multidimensional stochastic delay differential equations with normal reflection. The equations are driven by a fractional Brownian motion with Hurst parameter H > 1/2. The stochastic integral with respect to the fractional Brownian motion is a pathwise Riemann¿Stieltjes integral.

Criteria for hitting probabilities with applications to systems of stochastic wave equations

We develop several results on hitting probabilities of random fields which highlight the role of the dimension of the parameter space. This yields upper and lower bounds in terms of Hausdorff measure and Bessel-Riesz capacity, respectively. We apply these results to a system of stochastic wave equations in spatial dimension k >- 1 driven by a d-dimensional spatially homogeneous additive Gaussian noise that is white in time and colored in space.

Stochastic differential equations with random coefficients

In this paper we establish the existence and uniqueness of a solution for different types of stochastic differential equation with random initial conditions and random coefficients. The stochastic integral is interpreted as a generalized Stratonovich integral, and the techniques used to derive these results are mainly based on the path properties of the Brownian motion, and the definition of the Stratonovich integral.

Large deviations for stochastic Volterra equations

This paper is devoted to prove a large-deviation principle for solutions to multidimensional stochastic Volterra equations.

Stochastic delay differential equations driven by fractional Brownian motion with Hurst parameter H 1/2

We consider the Cauchy problem for a stochastic delay differential equation driven by a fractional Brownian motion with Hurst parameter H>¿. We prove an existence and uniqueness result for this problem, when the coefficients are sufficiently regular. Furthermore, if the diffusion coefficient is bounded away from zero and the coefficients are smooth functions with bounded derivatives of all orders, we prove that the law of the solution admits a smooth density with respect to Lebesgue measure on R.

Carbohydrate and nitrogen stores in Festuca paniculata under mowing explain dominance in subalpine grasslands

Cessation of traditional management threatens semi-natural grassland diversity through the colonisation or increase of competitive species adapted to nutrient-poor conditions. Regular mowing is one practice that controls their abundance. This study evaluated the ecophysiological mechanisms limiting short- and long-term recovery after mowing for Festuca paniculata, a competitive grass that takes over subalpine grasslands in the Alps following cessation of mowing. We quantified temporal variations in carbon (C) and nitrogen (N) content, starch, fructan and total soluble sugars in leaves, stem bases and roots of F. paniculata during one growth cycle in mown and unmown fields and related them to the dynamics of soil mineral N concentration and soil moisture. Short-term results suggest that the regrowth of F. paniculata following mowing might be N-limited, first because of N dilution by C increments in the plant tissue, and second, due to low soil mineral N and soil moisture at this time of year. However, despite short-term effects of mowing on plant growth, C and N content and concentration at the beginning of the following growing season were not affected. Nevertheless, total biomass accumulation at peak standing biomass was largely reduced compared to unmown fields. Moreover, lower C storage capacity at the end of the growing season impacted C allocation to vegetative reproduction during winter, thereby dramatically limiting the horizontal growth of F. paniculata tussocks in the long term. We conclude that mowing reduces the growth of F. paniculata tussocks through both C and N limitation. Such results will help understanding how plant responses to defoliation regulate competitive interactions within plant communities.

Stochastic models and numerical algorithms for a class of regulatory gene networks.

Regulatory gene networks contain generic modules, like those involving feedback loops, which are essential for the regulation of many biological functions (Guido et al. in Nature 439:856-860, 2006). We consider a class of self-regulated genes which are the building blocks of many regulatory gene networks, and study the steady-state distribution of the associated Gillespie algorithm by providing efficient numerical algorithms. We also study a regulatory gene network of interest in gene therapy, using mean-field models with time delays. Convergence of the related time-nonhomogeneous Markov chain is established for a class of linear catalytic networks with feedback loops.

An allele-specific, stochastic gene expression process controls the expression of multiple Ly49 family genes and generates a diverse, MHC-specific NK cell receptor repertoire.

Mouse NK cells express MHC class I-specific inhibitory Ly49 receptors. Since these receptors display distinct ligand specificities and are clonally distributed, their expression generates a diverse NK cell receptor repertoire specific for MHC class I molecules. We have previously found that the Dd (or Dk)-specific Ly49A receptor is usually expressed from a single allele. However, a small fraction of short-term NK cell clones expressed both Ly49A alleles, suggesting that the two Ly49A alleles are independently and randomly expressed. Here we show that the genes for two additional Ly49 receptors (Ly49C and Ly49G2) are also expressed in a (predominantly) mono-allelic fashion. Since single NK cells can co-express multiple Ly49 receptors, we also investigated whether mono-allelic expression from within the tightly linked Ly49 gene cluster is coordinate or independent. Our clonal analysis suggests that the expression of alleles of distinct Ly49 genes is not coordinate. Thus Ly49 alleles are apparently independently and randomly chosen for stable expression, a process that directly restricts the number of Ly49 receptors expressed per single NK cell. We propose that the Ly49 receptor repertoire specific for MHC class I is generated by an allele-specific, stochastic gene expression process that acts on the entire Ly49 gene cluster.

Stochastic resonance in a dipole

We show that the dipole, a system usually proposed to model relaxation phenomena, exhibits a maximum in the signal-to-noise ratio at a nonzero noise level, thus indicating the appearance of stochastic resonance. The phenomenon occurs in two different situations, i.e., when the minimum of the potential of the dipole remains fixed in time and when it switches periodically between two equilibrium points. We have also found that the signal-to-noise ratio has a maximum for a certain value of the amplitude of the oscillating field.

Initiation and limitation of Ly-49A NK cell receptor acquisition by T cell factor-1.

The establishment of clonally variable expression of MHC class I-specific receptors by NK cells is not well understood. The Ly-49A receptor is used by approximately 20% of NK cells, whereby most cells express either the maternal or paternal allele and few express simultaneously both alleles. We have previously shown that NK cells expressing Ly-49A were reduced or almost absent in mice harboring a single or no functional allele of the transcription factor T cell factor-1 (TCF-1), respectively. In this study, we show that enforced expression of TCF-1 in transgenic mice yields an expanded Ly-49A subset. Even though the frequencies of Ly-49A(+) NK cells varied as a function of the TCF-1 dosage, the relative abundance of mono- and biallelic Ly-49A cells was maintained. Mono- and biallelic Ly-49A NK cells were also observed in mice expressing exclusively a transgenic TCF-1, i.e., expressing a fixed amount of TCF-1 in all NK cells. These findings suggest that Ly-49A acquisition is a stochastic event due to limiting TCF-1 availability, rather than the consequence of clonally variable expression of the endogenous TCF-1 locus. Efficient Ly-49A acquisition depended on the expression of a TCF-1 isoform, which included a domain known to associate with the TCF-1 coactivator beta-catenin. Indeed, the proximal Ly-49A promoter was beta-catenin responsive in reporter gene assays. We thus propose that Ly-49A receptor expression is induced from a single allele in occasional NK cells due to a limitation in the amount of a transcription factor complex requiring TCF-1.

Stochastic inversion of tracer test and electrical geophysical data to estimate hydraulic conductivities.

Quantifying the spatial configuration of hydraulic conductivity (K) in heterogeneous geological environments is essential for accurate predictions of contaminant transport, but is difficult because of the inherent limitations in resolution and coverage associated with traditional hydrological measurements. To address this issue, we consider crosshole and surface-based electrical resistivity geophysical measurements, collected in time during a saline tracer experiment. We use a Bayesian Markov-chain-Monte-Carlo (McMC) methodology to jointly invert the dynamic resistivity data, together with borehole tracer concentration data, to generate multiple posterior realizations of K that are consistent with all available information. We do this within a coupled inversion framework, whereby the geophysical and hydrological forward models are linked through an uncertain relationship between electrical resistivity and concentration. To minimize computational expense, a facies-based subsurface parameterization is developed. The Bayesian-McMC methodology allows us to explore the potential benefits of including the geophysical data into the inverse problem by examining their effect on our ability to identify fast flowpaths in the subsurface, and their impact on hydrological prediction uncertainty. Using a complex, geostatistically generated, two-dimensional numerical example representative of a fluvial environment, we demonstrate that flow model calibration is improved and prediction error is decreased when the electrical resistivity data are included. The worth of the geophysical data is found to be greatest for long spatial correlation lengths of subsurface heterogeneity with respect to wellbore separation, where flow and transport are largely controlled by highly connected flowpaths.