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Non-symmetric hitting distributions on the hyperbolic half-plane and subordinated perpetuities.

Paolo Baldi, Enrico Casadio Tarabusi, Alessandro Figà-Talamanca, Marc Yor (2001)

Revista Matemática Iberoamericana

We study the law of functionals whose prototype is ∫0+∞ eBs(ν) dWs(μ),where B(ν) and W(μ) are independent Brownian motions with drift. These functionals appear naturally in risk theory as well as in the study of in variant diffusions on the hyperbolic half-plane. Emphasis is put on the fact that the results are obtained in two independent, very different fashions (invariant diffusions on the hyperbolic half-plane and Bessel processes).

Normal martingales and polynomial families

H. Hammouch (2004)

Annales Polonici Mathematici

Wiener and compensated Poisson processes, as normal martingales, are associated to classical sequences of polynomials, namely Hermite polynomials for the first one and Charlier polynomials for the second. The problem studied in this paper is to find if there exist other normal martingales which are associated to classical sequences of polynomials. Privault, Solé and Vives [5] solved this problem via the quantum Kabanov formula under some assumptions on the normal martingales considered. We solve...

Norms for copulas.

Darsow, William F., Olsen, Elwood T. (1995)

International Journal of Mathematics and Mathematical Sciences

Nouveaux résultats sur les petites perturbations d’équations d’évolutions aléatoires

Lyliane Irène Rajaonarison, Toussaint Joseph Rabeherimanana (2012)

Annales mathématiques Blaise Pascal

Dans cet article, nous étudions les résultats de grandes déviations associés au couple ( X ε , ν ε ) , solution de l’E.D.S. interprétée au sens d’Itô : d X t ε = ε σ ν ε ( t ) ( X t ε ) d W t + b ν ε ( t ) ( X t ε ) d t ; X 0 ε = x ∈ ℝ d avec des conditions assez générales sur les coefficients et dans les deux cas suivants :Premier cas : ν ε est indépendant du mouvement brownien W et satisfait à un principe de grandes déviations ;Deuxième cas : ν ε est un processus markovien avec un nombre fini d’états { 1 , . . . , n } vérifiant ℙ { ν ε ( t + Δ ) = j / ν ε ( t ) = i , X ε ( t ) = x } = d i j ( x ) Δ + o ( Δ ) uniformément dans ℝ d pourvu que Δ ↓ 0 , 1 ≤ i , j ≤ n , i ≠ j .Ces résultats sont des extensions de ceux de Bezuidenhout...

Number of hidden states and memory: a joint order estimation problem for Markov chains with Markov regime

Antoine Chambaz, Catherine Matias (2009)

ESAIM: Probability and Statistics

This paper deals with order identification for Markov chains with Markov regime (MCMR) in the context of finite alphabets. We define the joint order of a MCMR process in terms of the number k of states of the hidden Markov chain and the memory m of the conditional Markov chain. We study the properties of penalized maximum likelihood estimators for the unknown order (k, m) of an observed MCMR process, relying on information theoretic arguments. The novelty of our work relies in the joint...

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