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Decomposition of two parameter martingales.

David Nualart Rodón (1981)

Stochastica

In this paper we exhibit some decompositions in orthogonal stochastic integrals of two-parameter square integrable martingales adapted to a Brownian sheet which generalize the representation theorem of E. Wong and M. Zakai ([6]). Concretely, a development in a series of multiple stochastic integrals is obtained for such martingales. These results are applied for the characterization of martingales of path independent variation.

Defaultable bonds with an infinite number of Lévy factors

Jacek Jakubowski, Mariusz Niewęgłowski (2010)

Applicationes Mathematicae

A market with defaultable bonds where the bond dynamics is in a Heath-Jarrow-Morton setting and the forward rates are driven by an infinite number of Lévy factors is considered. The setting includes rating migrations driven by a Markov chain. All basic types of recovery are investigated. We formulate necessary and sufficient conditions (generalized HJM conditions) under which the market is arbitrage-free. Connections with consistency conditions are discussed.

Density estimation for one-dimensional dynamical systems

Clémentine Prieur (2001)

ESAIM: Probability and Statistics

In this paper we prove a Central Limit Theorem for standard kernel estimates of the invariant density of one-dimensional dynamical systems. The two main steps of the proof of this theorem are the following: the study of rate of convergence for the variance of the estimator and a variation on the Lindeberg–Rio method. We also give an extension in the case of weakly dependent sequences in a sense introduced by Doukhan and Louhichi.

Density Estimation for One-Dimensional Dynamical Systems

Clémentine Prieur (2010)

ESAIM: Probability and Statistics

In this paper we prove a Central Limit Theorem for standard kernel estimates of the invariant density of one-dimensional dynamical systems. The two main steps of the proof of this theorem are the following: the study of rate of convergence for the variance of the estimator and a variation on the Lindeberg–Rio method. We also give an extension in the case of weakly dependent sequences in a sense introduced by Doukhan and Louhichi.

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