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Self-stabilizing processes: uniqueness problem for stationary measures and convergence rate in the small-noise limit

Samuel Herrmann, Julian Tugaut (2012)

ESAIM: Probability and Statistics

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...

Semiorthogonal linear prewavelets on irregular meshes

Peter Oswald (2006)

Banach Center Publications

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 L p -condition, 1 < p < ∞, of such systems.

Sets with the Bernstein and generalized Markov properties

Mirosław Baran, Agnieszka Kowalska (2014)

Annales Polonici Mathematici

It is known that for C ∞ 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 C ∞ determining. In this paper we give examples of sets which are not C ∞ determining, but have the Bernstein and generalized Markov properties.

Shape-preserving properties and asymptotic behaviour of the semigroup generated by the Black-Scholes operator

Antonio Attalienti, Ioan Rasa (2008)

Czechoslovak Mathematical Journal

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 summability for Monge transport density via interpolation

Luigi De Pascale, Aldo Pratelli (2004)

ESAIM: Control, Optimisation and Calculus of Variations

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 L p source is also an L p function for any 1 ≤ p ≤ + ∞ .

Sharp summability for Monge Transport density via Interpolation

Luigi De Pascale, Aldo Pratelli (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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 1 ≤ p ≤ + ∞ .

Shift invariant operators and a saturation theorem

Karol Dziedziul (2003)

Applicationes Mathematicae

The properties of shift invariant operators Q h are proved: It is shown that Q has polynomial order r iff r is the rate of convergence of Q h . A weak saturation theorem is given. If f is replaced by Q f h in the weak saturation formula the asymptotics of the expression is calculated. Moreover, bootstrap approximation is introduced.

Currently displaying 1861 – 1880 of 2608