Generalized fractional smoothness and LpL_p-variation of BSDEs with non-Lipschitz terminal condition

We relate the $L_p$-variation, $2\le p < \infty$, of a solution of a backward stochastic differential equation with a path-dependent terminal condition to a generalized notion of fractional smoothness. This concept of fractional smoothness takes into account the quantitative propagation of singularities in time

Cluster structures on strata of flag varieties

We introduce some new Frobenius subcategories of the module category of a preprojective algebra of Dynkin type, and we show that they have a cluster structure in the sense of Buan-Iyama-Reiten-Scott. These categorical cluster structures yield cluster algebra structures in the coordinate rings of intersections of opposed Schubert cells.Comment: 31 pages, v.2 : a comment about the relation to Muller-Speyer conjecture on positroid varieties is added in 7.3. v.3. final version, to appear in Advances in Mat

Elemental and isotopic abundances in the solar wind

The use of collecting foils and lunar material to assay the isotopic composition of the solar wind is reviewed. Arguments are given to show that lunar surface correlated gases are likely to be most useful in studying the history of the solar wind, though the isotopic abundances are thought to give a good approximation to the solar wind composition. The results of the analysis of Surveyor material are also given. The conditions leading to a significant component of the interstellar gas entering the inner solar system are reviewed and suggestions made for experimental searches for this fraction. A critical discussion is given of the different ways in which the basic solar composition could be modified by fractionation taking place between the sun's surface and points of observation such as on the Moon or in interplanetary space. An extended review is made of the relation of isotopic and elemental composition of the interplanetary gas to the dynamic behavior of the solar corona, especially processes leading to fractionation. Lastly, connection is made between the subject of composition, nucleosynthesis and the convective zone of the sun, and processes leading to modification of initial accretion of certain gases on the Earth and Moon

Study on determining stability domains for nonlinear dynamical systems Quarterly progress report no. 1, 1 May - 1 Aug. 1966

Numerical algorithm for determining stability domain of attraction of equilibrium motions of nonlinear dynamical systems - Liapunov function

On fractional smoothness and LpL_p-approximation on the Gaussian space

We consider Gaussian Besov spaces obtained by real interpolation and Riemann-Liouville operators of fractional integration on the Gaussian space and relate the fractional smoothness of a functional to the regularity of its heat extension. The results are applied to study an approximation problem in $L_p$ for $2\le p<\infty$ for stochastic integrals with respect to the $d$-dimensional (geometric) Brownian motion.Comment: Published in at http://dx.doi.org/10.1214/13-AOP884 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Existence, Uniqueness and Comparison Results for BSDEs with L\'evy Jumps in an Extended Monotonic Generator Setting

We show existence of a unique solution and a comparison theorem for a one-dimensional backward stochastic differential equation with jumps that emerge from a L\'evy process. The considered generators obey a time-dependent extended monotonicity condition in the y-variable and have linear time-dependent growth. Within this setting, the results generalize those of Royer (2006), Yin and Mao (2008) and, in the $L^2$-case with linear growth, those of Kruse and Popier (2016). Moreover, we introduce an approximation technique: Given a BSDE driven by Brownian motion and Poisson random measure, we consider BSDEs where the Poisson random measure admits only jumps of size larger than $1/n$. We show convergence of their solutions to those of the original BSDE, as $n \to \infty.$ The proofs only rely on It\^o's formula and the Bihari-LaSalle inequality and do not use Girsanov transforms.Comment: Version 3 is the final, reviewed version as published in Probability, Uncertainty and Quantitative Ris

Type and cotype with respect to arbitrary orthonormal systems

Let \on_{k \in \nz} be an orthonormal system on some $\sigma$-finite measure space (\Om,p). We study the notion of cotype with respect to $\Phi$ for an operator $T$ between two Banach spaces $X$ and $Y$, defined by \fco T := \inf $c$ such that \Tfmm \pl \le \pl c \pll \gmm \hspace{.7cm}\mbox{for all}\hspace{.7cm} (x_k)\subset X \pl, where (g_k)_{k\in \nz} is a sequence of independent and normalized gaussian variables. It is shown that this $\Phi$-cotype coincides with the usual notion of cotype $2$ iff \linebreak \fco {I_{\lin}} \sim \sqrt{\frac{n}{\log (n+1)}} uniformly in $n$ iff there is a positive $\eta>0$ such that for all n \in \nz one can find an orthonormal \Psi = (\psi_l)_1^n \subset {\rm span}\{ \phi_k \p|\p k \in \nz\} and a sequence of disjoint measurable sets (A_l)_1^n \subset \Om with \int\limits_{A_l} \bet \psi_l\rag^2 d p \pl \ge \pl \eta \quad \mbox{for all}\quad l=1,...,n \pl. A similar result holds for the type situation. The study of type and cotype with respect to orthonormal systems of a given length provides the appropriate approach to this result. We intend to give a quite complete picture for orthonormal systems in measure space with few atoms