Symmetries of stochastic differential equations using Girsanov transformations

Aiming at enlarging the class of symmetries of an SDE, we introduce a family of stochastic transformations able to change also the underlying probability measure exploiting Girsanov Theorem and we provide new determining equations for the infinitesimal symmetries of the SDE. The well-defined subset of the previous class of measure transformations given by Doob transformations allows us to recover all the Lie point symmetries of the Kolmogorov equation associated with the SDE. This gives the first stochastic interpretation of all the deterministic symmetries of the Kolmogorov equation. The general theory is applied to some relevant stochastic models

Weak symmetries of stochastic differential equations driven by semimartingales with jumps

Stochastic symmetries and related invariance properties of \ufb01nite dimensional SDEs driven by general c`adl`ag semimartingales taking values in Lie groups are de\ufb01ned and investigated. The considered set of SDEs, \ufb01rst introduced by S. Cohen, includes a\ufb03ne and Marcus type SDEs as well as smooth SDEs driven by L\ub4evy processes and iterated random maps. A natural extension to this general setting of reduction and reconstruction theory for symmetric SDEs is provided. Our theorems imply as special cases non trivial invariance results concerning a class of a\ufb03ne iterated random maps as well as (weak) symmetries for numerical schemes (of Euler and Milstein type) for Brownian motion driven SDEs

A note on symmetries of diffusions within a martingale problem approach

A geometric reformulation of the martingale problem associated with a set of diffusion processes is proposed. This formulation, based on second-order geometry and It\uf4 integration on manifolds, allows us to give a natural and effective definition of Lie symmetries for diffusion processes

An entropy approach to Bose-Einstein condensation

A proper one-particle relative entropy is introduced for the ground state of trapped Bose particles and its asymptotic behavior under the GP scaling limit is investigated. Some peculiar properties of the relative entropy allow to prove an existence theorem for the probability measure associated to the GP functional and a related weak convergence result

Chemistry and Clay Mineralogy of Cores 8, 9, 10, New Harbor, Antarctica

Electrical conductivity and ionic composition of extracted solutions from ice-cemented permafrost from cores 8,9,and 10 show that most of the sediments were deposited in a marine environment and that aggradation of permafrost during exposure of the sediments to subaerial conditions caused ionic concentration. Influx of brines capable of moving in permafrost is also suggested. Regions of low conductivity are interpreted either as freshwater episodes or textural discontinuities. Clay mineralogy can be separated into three major assemblages corresponding to the three major lithological units. The clay minerals show little weathering and complex irregular interstratification of mica-vermiculite-montmorillonite and chlorite

Solution geochemistry and behaviour of major and trace elements during summer in a moss community at Edmonson Point, Victoria Land, Antarctica

Physical and chemical characteristics and solution geochemistry of major and trace elements were investigated in an area of volcanic soil colonized by mosses at Edmonson Point (central Victoria Land) during the international BIOTAS (Biological Investigations of Terrestrial Antarctic Systems) expedition (BIOTEX) in the 1995–96 summer. The broad objective was to study the environmental factors involved in plant colonisation and survival in terrestrial continental Antarctic ecosystems. The results showed that moss distribution and survival throughout the summer was closely dependent on water supply. In Antarctic coastal ecosystems the environmental biogeochemistry is largely dominated by ions of marine origin. At the drier end of a hydrological gradient the dry cushions of Hennediella heimii were encrusted with salts and showed much higher concentrations of soluble ions (Na+, Cl−, K+, Ca2+, Mg2+, SO42−, NO3−) than those in adhering soil particles or in other moss species from wetter parts of the transect. Although salt encrustations may partly derive from sublimation of surface snow, comparisons between concentrations of soluble ions in the dry moss and those in the < 2 mm fraction of surface and deep soil showed an upward migration along the soil profile of soluble ions as the substratum dried out, between December and January, and their accumulation mostly on mosses. At the wet end of the transect messes were less affected by salt encrustations and there was evidence of Ca2+ uptake and an active cycling of nutrients