Displaying similar documents to “Estimates for the distribution of the first exit time of α-stable processes”

Generalized tempered stable processes

Jan Rosiński, Jennifer L. Sinclair (2010)

Banach Center Publications

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This work introduces the class of generalized tempered stable processes which encompass variations on tempered stable processes that have been introduced in the field, including "modified tempered stable processes", "layered stable processes", and "Lamperti stable processes". Short and long time behavior of GTS Lévy processes is characterized and the absolute continuity of GTS processes with respect to the underlying stable processes is established. Series representations of GTS Lévy...

Stable-1/2 bridges and insurance

Edward Hoyle, Lane P. Hughston, Andrea Macrina (2015)

Banach Center Publications

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We develop a class of non-life reserving models using a stable-1/2 random bridge to simulate the accumulation of paid claims, allowing for an essentially arbitrary choice of a priori distribution for the ultimate loss. Taking an information-based approach to the reserving problem, we derive the process of the conditional distribution of the ultimate loss. The "best-estimate ultimate loss process" is given by the conditional expectation of the ultimate loss. We derive explicit expressions...

Stochastic flow for SDEs with jumps and irregular drift term

Enrico Priola (2015)

Banach Center Publications

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We consider non-degenerate SDEs with a β-Hölder continuous and bounded drift term and driven by a Lévy noise L which is of α-stable type. If β > 1 - α/2 and α ∈ [1,2), we show pathwise uniqueness and existence of a stochastic flow. We follow the approach of [Priola, Osaka J. Math. 2012] improving the assumptions on the noise L. In our previous paper L was assumed to be non-degenerate, α-stable and symmetric. Here we can also recover relativistic and truncated stable processes and...

On SαS density function

Grażyna Mazurkiewicz (2005)

Discussiones Mathematicae Probability and Statistics

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In this paper, we study some analytical properties of the symmetric α-stable density function.

Long memory and self-similar processes

Gennady Samorodnitsky (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

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This paper is a survey of both classical and new results and ideas on long memory, scaling and self-similarity, both in the light-tailed and heavy-tailed cases.

Around stable forking

Byunghan Kim, A. Pillay (2001)

Fundamenta Mathematicae

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We discuss various conjectures and problems around the issue of when and whether stable formulas are responsible for forking in simple theories. We prove that if the simple theory T has strong stable forking then any complete type is a nonforking extension of a complete type which is axiomatized by instances of stable formulas. We also give another treatment of the first author's result which identifies canonical bases in supersimple theories.

A Note on the Uniqueness of Stable Marriage Matching

Ewa Drgas-Burchardt (2013)

Discussiones Mathematicae Graph Theory

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In this note we present some sufficient conditions for the uniqueness of a stable matching in the Gale-Shapley marriage classical model of even size. We also state the result on the existence of exactly two stable matchings in the marriage problem of odd size with the same conditions.

Decompositions of saturated models of stable theories

M. C. Laskowski, S. Shelah (2006)

Fundamenta Mathematicae

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We characterize the stable theories T for which the saturated models of T admit decompositions. In particular, we show that countable, shallow, stable theories with NDOP have this property.