Zobrazeno 1 - 10
of 39
pro vyhledávání: '"Alili, Larbi"'
We are interested in the law of the first passage time of an Ornstein-Uhlenbeck process to time-varying thresholds. We show that this problem is connected to the laws of the first passage time of the process to members of a two-parameter family of fu
Externí odkaz:
http://arxiv.org/abs/2210.01658
Autor:
Woodford, David, Alili, Larbi
We provide results relating to the integrability, uniform integrability and local integrability of exponential MAPs, which are natural extensions of exponential Levy models. Then, we use Mellin transform and partial integro-differential equation meth
Externí odkaz:
http://arxiv.org/abs/1907.06596
Autor:
Alili, Larbi, Bartholmé, Carine, Chaumont, Loïc, Patie, Pierre, Savov, Mladen, Vakeroudis, Stavros
R. Doney identifies a striking factorization of the arc-sine law in terms of the suprema of two independent stable processes of the same index by an elegant random walks approximation. In this paper, we provide an alternative proof and a generalizati
Externí odkaz:
http://arxiv.org/abs/1905.12128
Autor:
Alili, Larbi, Woodford, David
Consider a Lamperti-Kiu Markov additive process $(J_t,\xi_t:t\geq0)$ on $\{+,-\}\times\mathbb{R}\cup\infty$ where $J$ is the modulating Markov chain component. First, we study the finiteness of the exponential functional and then consider its moments
Externí odkaz:
http://arxiv.org/abs/1811.10286
Autor:
Alili, Larbi, Matsumoto, Hiroyuki
We look at decompositions of perpetuities and apply that to the study of the distributions of hitting times of Bessel processes of two types of square root boundaries. These distributions are linked giving a new proof of some Mellin transforms result
Externí odkaz:
http://arxiv.org/abs/1709.08923
Let $X$ be a standard Markov process. We prove that a space inversion property of $X$ implies the existence of a Kelvin transform of $X$-harmonic, excessive and operator-harmonic functions and that the inversion property is inherited by Doob $h$-tran
Externí odkaz:
http://arxiv.org/abs/1704.00916
We show that any $\mathbb{R}^d\setminus\{0\}$-valued self-similar Markov process $X$, with index $\alpha>0$ can be represented as a path transformation of some Markov additive process (MAP) $(\theta,\xi)$ in $S_{d-1}\times\mathbb{R}$. This result ext
Externí odkaz:
http://arxiv.org/abs/1601.08056
We establish a link between the distribution of an exponential functional I and the undershoots of a subordinator, which is given in terms of the associated harmonic potential measure. This allows us to give a necessary and sufficient condition in te
Externí odkaz:
http://arxiv.org/abs/1310.4955
Autor:
Alili, Larbi, Patie, Pierre
Publikováno v:
Proc. Amer. Math. Soc. 142 (2014), 3811-3824
We start by introducing a nonlinear involution operator which maps the space of solutions of Sturm-Liouville equations into the space of solutions of the associated equations which turn out to be nonlinear ordinary differential equations. We study so
Externí odkaz:
http://arxiv.org/abs/1211.2222
Autor:
Alili, Larbi, Wu, Ching-Tang
We consider a class of linear Volterra transforms of Brownian motion associated to a sequence of M\"untz Gaussian spaces and determine explicitly their kernels; some interesting links with M\"untz-Legendre polynomials are provided. This gives new exp
Externí odkaz:
http://arxiv.org/abs/1112.4071