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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 estimates for the Ornstein-Uhlenbeck operator

Giancarlo Mauceri, Stefano Meda, Peter Sjögren (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Let be the Ornstein-Uhlenbeck operator which is self-adjoint with respect to the Gauss measure γ on d . We prove a sharp estimate of the operator norm of the imaginary powers of on L p ( γ ) , 1 < p < ...

Signals generated in memristive circuits

Artur Sowa (2012)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

Signals generated in circuits that include nano-structured elements typically have strongly distinct characteristics, particularly the hysteretic distortion. This is due to memristance, which is one of the key electronic properties of nanostructured materials. In this article, we consider signals generated from a memrsitive circuit model. We demonstrate numerically that such signals can be efficiently represented in certain custom-designed nonorthogonal bases. The proposed method ensures that the...

Solvability Conditions for a Linearized Cahn-Hilliard Equation of Sixth Order

V. Vougalter, V. Volpert (2012)

Mathematical Modelling of Natural Phenomena

We obtain solvability conditions in H6(ℝ3) for a sixth order partial differential equation which is the linearized Cahn-Hilliard problem using the results derived for a Schrödinger type operator without Fredholm property in our preceding article [18].

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