Schwach verkoppelte Ungleichungssysteme und konvexe Spline-Interpolation.
Self-stabilizing processes: uniqueness problem for stationary measures and convergence rate in the small-noise limit
In the context of self-stabilizing processes, that is processes attracted by their own law, living in a potential landscape, we investigate different properties of the invariant measures. The interaction between the process and its law leads to nonlinear stochastic differential equations. In [S. Herrmann and J. Tugaut. Electron. J. Probab. 15 (2010) 2087–2116], the authors proved that, for linear interaction and under suitable conditions, there exists a unique symmetric limit measure associated...
Self-stabilizing processes: uniqueness problem for stationary measures and convergence rate in the small-noise limit
In the context of self-stabilizing processes, that is processes attracted by their own law, living in a potential landscape, we investigate different properties of the invariant measures. The interaction between the process and its law leads to nonlinear stochastic differential equations. In [S. Herrmann and J. Tugaut. Electron. J. Probab. 15 (2010) 2087–2116], the authors proved that, for linear interaction and under suitable conditions, there...
Semiclassical analysis and a new result for Poisson-Lev́y excursion measures.
Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model.
Semiclassical quantization of circular billiard in homogeneous magnetic field: Berry-Tabor approach.
Semigroup-theoretical proofs of the central limit theorem and other theorems of analysis.
Semiorthogonal linear prewavelets on irregular meshes
We extend results on constructing semiorthogonal linear spline prewavelet systems in one and two dimensions to the case of irregular dyadic refinement. In the one-dimensional case, we obtain sharp two-sided inequalities for the -condition, 1 < p < ∞, of such systems.
Sets of divergence of Taylor series and of trigonometric series
Sets with the Bernstein and generalized Markov properties
It is known that for determining sets Markov’s property is equivalent to Bernstein’s property. We are interested in finding a generalization of this fact for sets which are not determining. In this paper we give examples of sets which are not determining, but have the Bernstein and generalized Markov properties.
Shape preserving rational cubic interpolation.
Shape-preserving multivariate polynomial approximation in .
Shape-preserving properties and asymptotic behaviour of the semigroup generated by the Black-Scholes operator
The paper is devoted to a careful analysis of the shape-preserving properties of the strongly continuous semigroup generated by a particular second-order differential operator, with particular emphasis on the preservation of higher order convexity and Lipschitz classes. In addition, the asymptotic behaviour of the semigroup is investigated as well. The operator considered is of interest, since it is a unidimensional Black-Scholes operator so that our results provide qualitative information on the...
Sharp error bounds for some quadrature formulae and applications.
Sharp error bounds for the trapezoidal rule and Simpson's rule.
Sharp Estimates in Terms of Moduli of Smoothness for Compound Cubature Rules.
Sharp Grüss-type inequalities for functions whose derivatives are of bounded variation.
Sharp summability for Monge transport density via interpolation
Using some results proved in De Pascale and Pratelli [Calc. Var. Partial Differ. Equ. 14 (2002) 249-274] (and De Pascale et al. [Bull. London Math. Soc. 36 (2004) 383-395]) and a suitable interpolation technique, we show that the transport density relative to an source is also an function for any .
Sharp summability for Monge Transport density via Interpolation
Using some results proved in De Pascale and Pratelli [Calc. Var. Partial Differ. Equ.14 (2002) 249-274] (and De Pascale et al. [Bull. London Math. Soc.36 (2004) 383-395]) and a suitable interpolation technique, we show that the transport density relative to an Lp source is also an Lp function for any .
Sharpness of estimates for the least uniform derivation from the class of functions with bounded second derivative.