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Displaying 101 – 120 of 125

Stochastic flow for SDEs with jumps and irregular drift term

Enrico Priola (2015)

Banach Center Publications

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 some classes...

Support d'une équation d'Itô avec sauts en dimension 1

Thomas Simon (2002)

Séminaire de probabilités de Strasbourg

Support of a Marcus equation in dimension 1.

Simon, Thomas (2000)

Electronic Communications in Probability [electronic only]

Synchronization of dissipative dynamical systems driven by non-Gaussian Lev́y noises.

Liu, Xianming, Duan, Jinqiao, Liu, Jicheng, Kloeden, Peter E. (2010)

International Journal of Stochastic Analysis

Tail asymptotics for exponential functionals of Lévy processes: The convolution equivalent case

Víctor Rivero (2012)

Annales de l'I.H.P. Probabilités et statistiques

We determine the rate of decrease of the right tail distribution of the exponential functional of a Lévy process with a convolution equivalent Lévy measure. Our main result establishes that it decreases as the right tail of the image under the exponential function of the Lévy measure of the underlying Lévy process. The method of proof relies on fluctuation theory of Lévy processes and an explicit pathwise representation of the exponential functional as the exponential functional of a bivariate subordinator....

Taux de croissance d'un subordinateur à double indice

Sandrine Lagaize (1999)

Annales de la Faculté des sciences de Toulouse : Mathématiques

The convex minorant of the Cauchy process.

Bertoin, Jean (2000)

Electronic Communications in Probability [electronic only]

The Donsker delta function of a Lévy process with application to chaos expansion of local time

Sure Mataramvura, Bernt Øksendal, Frank Proske (2004)

Annales de l'I.H.P. Probabilités et statistiques

The joint law of ages and residual lifetimes for two schemes of nested regenerative sets.

Lambert, Amaury (2001)

Electronic Journal of Probability [electronic only]

The law of the hitting times to points by a stable Lev́y process with no negative jumps.

Peskir, Goran (2008)

Electronic Communications in Probability [electronic only]

The lower envelope of positive self-similar Markov processes.

Chaumont, Loic, Millan, Juan Carlos Pardo (2006)

Electronic Journal of Probability [electronic only]

The pricing of credit risky securities under stochastic interest rate model with default correlation

Anjiao Wang, Zhong Xing Ye (2013)

Applications of Mathematics

In this paper, we study the pricing of credit risky securities under a three-firms contagion model. The interacting default intensities not only depend on the defaults of other firms in the system, but also depend on the default-free interest rate which follows jump diffusion stochastic differential equation, which extends the previous three-firms models (see R. A. Jarrow and F. Yu (2001), S. Y. Leung and Y. K. Kwok (2005), A. Wang and Z. Ye (2011)). By using the method of change of measure and...

Théorèmes limites avec poids pour les martingales vectorielles à temps continu

Faouzi Chaabane, Ahmed Kebaier (2008)

ESAIM: Probability and Statistics

On développe une approche générale du théorème limite centrale presque-sûre pour les martingales vectorielles quasi-continues à gauche convenablement normalisées dont on dégage une extension quadratique et un nouveau théorème de la limite centrale. L'application de ce résultat à l'estimation de la variance d'un processus à accroissements indépendants et stationnaires illustre l'usage qu'on peut en faire en statistique.

Time dependent subordination and Markov processes with jumps

Masao Nagasawa, Hiroshi Tanaka (2000)

Séminaire de probabilités de Strasbourg

Transience and non-explosion of certain stochastic Newtonian systems.

Kolokol'tsov, V.N., Schilling, R.L., Tyukov, A.E. (2002)

Electronic Journal of Probability [electronic only]

Two results on continuity and boundedness of stochastic convolutions

Stanisław Kwapień, Michael B. Marcus, Jan Rosiński (2006)

Annales de l'I.H.P. Probabilités et statistiques

Ultrafast Subordinators and Their Hitting Times

Mihály Kovács, Mark M. Meerschaert (2006)

Publications de l'Institut Mathématique

Un critère de tension dans les espaces de Besov-Orlicz et applications au problème du temps d’occupation

Mohamed Ait Ouahra, Abdelghani Kissami, Aissa Sghir (2011)

Annales mathématiques Blaise Pascal

Dans ce travail, nous présentons une nouvelle caractérisation de la norme des espaces de Besov-Orlicz associés à la $𝒩$ -fonction exponentielle $M_{β}$ pour $β > 0$ . Nous utilisons cette nouvelle norme et un lemme de Marcus et Pisier [15], pour démontrer un critère de tension et de régularité dans les espaces de Besov-Orlicz pour $β \geq 1$ . Nous étudions ensuite dans les espaces de Besov-Orlicz pour $β = 1$ , des théorèmes limites pour les mesures d’occupations du temps local du processus stable symétrique d’indice $1 < α \leq 2$ , ce qui...

Universality of the asymptotics of the one-sided exit problem for integrated processes

Frank Aurzada, Steffen Dereich (2013)

Annales de l'I.H.P. Probabilités et statistiques

We consider the one-sided exit problem – also called one-sided barrier problem – for ( $α$ -fractionally) integrated random walks and Lévy processes. Our main result is that there exists a positive, non-increasing function $α \mapsto θ (α)$ such that the probability that any $α$ -fractionally integrated centered Lévy processes (or random walk) with some finite exponential moment stays below a fixed level until time $T$ behaves as $T^{- θ (α) + o (1)}$ for large $T$ . We also investigate when the fixed level can be replaced by a different barrier...

Valuation of two-factor options under the Merton jump-diffusion model using orthogonal spline wavelets

Černá, Dana (2023)

Programs and Algorithms of Numerical Mathematics

This paper addresses the two-asset Merton model for option pricing represented by non-stationary integro-differential equations with two state variables. The drawback of most classical methods for solving these types of equations is that the matrices arising from discretization are full and ill-conditioned. In this paper, we first transform the equation using logarithmic prices, drift removal, and localization. Then, we apply the Galerkin method with a recently proposed orthogonal cubic spline-wavelet...

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