Stochastic representation of solutions to degenerate elliptic and parabolic boundary value and obstacle problems with Dirichlet boundary conditions

We prove existence and uniqueness of stochastic representations for solutions to elliptic and parabolic boundary value and obstacle problems associated with a degenerate Markov diffusion process. In particular, our article focuses on the Heston stochastic volatility process, which is widely used as an asset price model in mathematical finance and a paradigm for a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square root of the distance to the boundary of the half-plane. The generator of this process with killing, called the elliptic Heston operator, is a second-order, degenerate, elliptic partial differential operator whose coefficients have linear growth in the spatial variables and where the degeneracy in the operator symbol is proportional to the distance to the boundary of the half-plane. In mathematical finance, solutions to terminal/boundary value or obstacle problems for the parabolic Heston operator correspond to value functions for American-style options on the underlying asset.Comment: 47 pages; to appear in Transactions of the American Mathematical Societ

A HOLISTIC APPROACH OF RELATIONSHIP MARKETING IN LAUNCHING LUXURY NEW PRODUCTS

On the basis of increased complexity of the exchange mechanism, at the beginning of the third millennium the contemporary marketing suffers some physiognomic changes. Holistic orientation of the contemporary marketing is imposed by the new dimensions therelationship marketing, holistic marketing, luxury marketing, residential complex, research on perception of luxury

Schauder a priori estimates and regularity of solutions to boundary-degenerate elliptic linear second-order partial differential equations

We establish Schauder a priori estimates and regularity for solutions to a class of boundary-degenerate elliptic linear second-order partial differential equations. Furthermore, given a smooth source function, we prove regularity of solutions up to the portion of the boundary where the operator is degenerate. Degenerate-elliptic operators of the kind described in our article appear in a diverse range of applications, including as generators of affine diffusion processes employed in stochastic volatility models in mathematical finance, generators of diffusion processes arising in mathematical biology, and the study of porous media.Comment: 58 pages, 1 figure. To appear in the Journal of Differential Equations. Incorporates final galley proof corrections corresponding to published versio

New rr-Matrices for Lie Bialgebra Structures over Polynomials

For a finite dimensional simple complex Lie algebra $\mathfrak{g}$, Lie bialgebra structures on $\mathfrak{g}[[u]]$ and $\mathfrak{g}[u]$ were classified by Montaner, Stolin and Zelmanov. In our paper, we provide an explicit algorithm to produce $r$-matrices which correspond to Lie bialgebra structures over polynomials

Chiral molecular conductors based on methylated TTF derivatives

International audienc

Straightforward synthesis and insights of the photophysical properties of tetrathiafulvalene-acceptors (TTF-A)

International audienc

Particle methods for a virtual patient

The particle systems approach is a well known technique in computer graphics for modelling fuzzy objects such as fire and clouds. The algorithm has also been applied to different biomedical applications and this paper presents two such methods: a charged particle method for soft tissue deformation with integrated haptics; and a blood flow visualization technique based on boids. The goal is real time performance with high fidelity results

Reply to Comment of Gazdzicki and Heinz on Strangeness Enhancement in p+Ap+A and S+AS+A

The Comment of Gazdzicki and Heinz is flawed because their assumed baryon stopping power in $pA$ is inconsistent with data and because they ignored half the analysis based on the VENUS model. The Comment continues the misleading presentation of strangeness enhancement by focusing on ratios of integrated yields. Those ratios discard essential experimental information on the rapidity dependence of produced $\Lambda$ and obscure discrepancies between different data sets. Our conclusion remains that the NA35 minimum bias data on $p+S\rightarrow\Lambda +X$ indicate an anomalous enhancement of central rapidity strangeness in few nucleon reactions that points to non-equilibrium dynamics as responsible for strangeness enhancement in nuclear reactions.Comment: revtex file, 6 pages, submitted to Phys. Rev.