Semigroup theory applied to options.
Soit un espace riemannien symétrique et l’espace des fonctions continues sur tendant vers 0 à l’infini. On démontre qu’un opérateur , invariant par les isométries de , engendre un semi-groupe fortement continu de contractions sur s’il est dissipatif et si son domaine contient les fonctions de classe à support compact.
Let be domain in a complex Banach space , and let be a pseudometric assigned to by a Schwarz-Pick system. In the first section of the paper we establish several criteria for a mapping to be a generator of a -nonexpansive semigroup on in terms of its nonlinear resolvent. In the second section we let be a complex Hilbert space, the open unit ball of , and the hyperbolic metric on . We introduce the notion of a -monotone mapping and obtain simple characterizations of generators...
The aim of the paper is two-fold. First, we investigate the ψ-Bessel potential spaces on and study some of their properties. Secondly, we consider the fractional powers of an operator of the form , , where is an operator with real continuous negative definite symbol ψ: ℝⁿ → ℝ. We define the domain of the operator and prove that with this domain it generates an -sub-Markovian semigroup.
Let be a locally compact Hausdorff space. Let , i = 0,1,...,N, be generators of Feller semigroups in C₀() with related Feller processes and let , i = 0,...,N, be non-negative continuous functions on with . Assume that the closure A of defined on generates a Feller semigroup T(t), t ≥ 0 in C₀(). A natural interpretation of a related Feller process X = X(t), t ≥ 0 is that it evolves according to the following heuristic rules: conditional on being at a point p ∈ , with probability , the process...