Limit Theorems for Affine Markov Walks Conditioned to Stay Positive - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques Année : 2018

Limit Theorems for Affine Markov Walks Conditioned to Stay Positive

Résumé

Consider the real Markov walk $S_n = X_1+ \dots+ X_n$ with increments $\left(X_n\right)_{n\geqslant 1}$ defined by a stochastic recursion starting at $X_0=x$. For a starting point $y>0$ denote by $\tau_y$ the exit time of the process $\left( y+S_n \right)_{n\geqslant 1}$ from the positive part of the real line. We investigate the asymptotic behaviour of the probability of the event $\tau_y \geqslant n$ and of the conditional law of $y+S_n$ given $\tau_y \geqslant n$ as $n \to +\infty$.

Dates et versions

hal-01264999 , version 1 (30-01-2016)

Identifiants

Citer

Ion Grama, Ronan Lauvergnat, Emile Le Page. Limit Theorems for Affine Markov Walks Conditioned to Stay Positive. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2018, 54 (1), pp.529-568. ⟨10.1214/16-AIHP814⟩. ⟨hal-01264999⟩
117 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More