Mean Motion in Stochastic Plasmas With a Space-Dependent Diffusion Coefficient

Radial transport in the tokamap, which has been proposed as a simple model for the motion in a stochastic plasma, is investigated. A theory for previous numerical findings is presented. The new results are stimulated by the fact that the radial diffusion coefficients is space-dependent. The space-dependence of the transport coefficient has several interesting effects which have not been elucidated so far. Among the new findings are the analytical predictions for the scaling of the mean radial displacement with time and the relation between the Fokker-Planck diffusion coefficient and the diffusion coefficient from the mean square displacement. The applicability to other systems is also discussed. (c) 2009 WILEY-VCH GmbH & Co. KGaA, Weinheim

STABILITY ANALYSIS WITH APPLICATIONS OF A TWO-DIMENSIONAL DYNAMICAL SYSTEM ARISING FROM A STOCHASTIC MODEL FOR AN ASSET MARKET

We analyze the stability properties of equilibrium solutions and periodicity of orbits in a two-dimensional dynamical system whose orbits mimic the evolution of the price of an asset and the excess demand for that asset. The construction of the system is grounded upon a heterogeneous interacting agent model for a single risky asset market. An advantage of this construction procedure is that the resulting dynamical system becomes a macroscopic market model which mirrors the market quantities and qualities that would typically be taken into account solely at the microscopic level of modeling. The system`s parameters correspond to: (a) the proportion of speculators in a market; (b) the traders` speculative trend; (c) the degree of heterogeneity of idiosyncratic evaluations of the market agents with respect to the asset`s fundamental value; and (d) the strength of the feedback of the population excess demand on the asset price update increment. This correspondence allows us to employ our results in order to infer plausible causes for the emergence of price and demand fluctuations in a real asset market. The employment of dynamical systems for studying evolution of stochastic models of socio-economic phenomena is quite usual in the area of heterogeneous interacting agent models. However, in the vast majority of the cases present in the literature, these dynamical systems are one-dimensional. Our work is among the few in the area that construct and study analytically a two-dimensional dynamical system and apply it for explanation of socio-economic phenomena.

Symmetry in biology: from genetic code to stochastic gene regulation

Mathematical models, as instruments for understanding the workings of nature, are a traditional tool of physics, but they also play an ever increasing role in biology - in the description of fundamental processes as well as that of complex systems. In this review, the authors discuss two examples of the application of group theoretical methods, which constitute the mathematical discipline for a quantitative description of the idea of symmetry, to genetics. The first one appears, in the form of a pseudo-orthogonal (Lorentz like) symmetry, in the stochastic modelling of what may be regarded as the simplest possible example of a genetic network and, hopefully, a building block for more complicated ones: a single self-interacting or externally regulated gene with only two possible states: ` on` and ` off`. The second is the algebraic approach to the evolution of the genetic code, according to which the current code results from a dynamical symmetry breaking process, starting out from an initial state of complete symmetry and ending in the presently observed final state of low symmetry. In both cases, symmetry plays a decisive role: in the first, it is a characteristic feature of the dynamics of the gene switch and its decay to equilibrium, whereas in the second, it provides the guidelines for the evolution of the coding rules.

Environmental Objectives, Cost Efficiency, and Multivariate Stochastic Control

This paper is concerned with the cost efficiency in achieving the Swedish national air quality objectives under uncertainty. To realize an ecologically sustainable society, the parliament has approved a set of interim and long-term pollution reduction targets. However, there are considerable quantification uncertainties on the effectiveness of the proposed pollution reduction measures. In this paper, we develop a multivariate stochastic control framework to deal with the cost efficiency problem with multiple pollutants. Based on the cost and technological data collected by several national authorities, we explore the implications of alternative probabilistic constraints. It is found that a composite probabilistic constraint induces considerably lower abatement cost than separable probabilistic restrictions. The trend is reinforced by the presence of positive correlations between reductions in the multiple pollutants.

Stochastic Assessment Of Environmental Flows In Semiarid Environments

The regimen of environmental flows (EF) must be included as terms of environmental demand in the management of water resources. Even though there are numerous methods for the computation of EF, the criteria applied at different steps in the calculation process are quite subjective whereas the results are fixed values that must be meet by water planners. This study presents a friendly-user tool for the assessment of the probability of compliance of a certain EF scenario with the natural regimen in a semiarid area in southern Spain. 250 replications of a 25-yr period of different hydrological variables (rainfall, minimum and maximum flows, ...) were obtained at the study site from the combination of Monte Carlo technique and local hydrological relationships. Several assumptions are made such as the independence of annual rainfall from year to year and the variability of occurrence of the meteorological agents, mainly precipitation as the main source of uncertainty. Inputs to the tool are easily selected from a first menu and comprise measured rainfall data, EF values and the hydrological relationships for at least a 20-yr period. The outputs are the probabilities of compliance of the different components of the EF for the study period. From this, local optimization can be applied to establish EF components with a certain level of compliance in the study period. Different options for graphic output and analysis of results are included in terms of graphs and tables in several formats. This methodology turned out to be a useful tool for the implementation of an uncertainty analysis within the scope of environmental flows in water management and allowed the simulation of the impacts of several water resource development scenarios in the study site.

Volatility modelling in the forex market: an empirical evaluation

We compare three frequently used volatility modelling techniques: GARCH, Markovian switching and cumulative daily volatility models. Our primary goal is to highlight a practical and systematic way to measure the relative effectiveness of these techniques. Evaluation comprises the analysis of the validity of the statistical requirements of the various models and their performance in simple options hedging strategies. The latter puts them to test in a "real life" application. Though there was not much difference between the three techniques, a tendency in favour of the cumulative daily volatility estimates, based on tick data, seems dear. As the improvement is not very big, the message for the practitioner - out of the restricted evidence of our experiment - is that he will probably not be losing much if working with the Markovian switching method. This highlights that, in terms of volatility estimation, no clear winner exists among the more sophisticated techniques.