Degenerate Evolution Equations in Weighted Continuous Function Spaces, Markov Processes and the Black-Scholes Equation-Part II

“…Our interest now is to establish some new sets of conditions for the existence and the uniqueness of solutions of problems (3.1)-(3.2). Our results would be compared with those of Section 4 of [1].…”

Section: An Application To the Black-scholes Equationmentioning

confidence: 99%

Positive Semigroups Generated by Degenerate Second-Order Differential Operators

Altomare

Musceo

2008

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Abstract. In this paper we deal with degenerate second-order di¤erential operators in the framework of weighted continuous function spaces on a real interval. We show that, under particular boundary conditions, such operators generate positive strongly continuous semigroups which are the transition semigroups associated with suitable Markov processes. Finally an application to the Black-Scholes equation is also discussed.

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“…We shall apply Theorems 2.3 and 2.6 of [3] and, to this end, it is enough to verify conditions (2.6), (2.7) and (2.8) of that paper.…”

Section: Moreover the Restrictions Of (T M (T)) T 0 To The Spacesmentioning

confidence: 99%

“…In addition, by using results of [2,3], we show that the semigroup is the transition semigroup of a continuous Markov process on [0, +∞].…”

Section: Introductionmentioning

confidence: 98%

On a class of exponential-type operators and their limit semigroups

Altomare

Raşa

2005

Journal of Approximation Theory

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The paper is mainly focused upon the study of a class of second order degenerate elliptic operators on unbounded intervals.We show that these operators generate strongly continuous semigroups in suitable weighted spaces of continuous functions.Furthermore, we represent the semigroups as limits of iterates of the so-called exponential-type operators.In a particular case, starting from the stochastic differential equations associated with these operators, we also find an integral representation of the semigroup and determine its asymptotic behaviour.

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Degenerate Evolution Equations in Weighted Continuous Function Spaces, Markov Processes and the Black-Scholes Equation-Part II

Cited by 12 publications

References 11 publications

Degenerate differential equations and modified Szász-Mirakjan operators

Degenerate differential equations and modified Szász-Mirakjan operators

Positive Semigroups Generated by Degenerate Second-Order Differential Operators

On a class of exponential-type operators and their limit semigroups

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