Central limit theorems for super Ornstein-Uhlenbeck processes

DOI10.1007/s10440-013-9837-0zbMath1301.60027arXiv1302.1254OpenAlexW2146393238MaRDI QIDQ461344

Rui Zhang, Renming Song, Yan-Xia Ren

Publication date: 10 October 2014

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.1254

zbMATH Keywords

Ornstein-Uhlenbeck processcentral limit theorembranching processsuperprocessbackbone decompositionbranching Ornstein-Uhlenbeck processsuper Ornstein-Uhlenbeck process

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Probabilistic potential theory (60J45) Random measures (60G57) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items (8)

Stable central limit theorems for super Ornstein-Uhlenbeck processes. II. ⋮ Functional central limit theorems for supercritical superprocesses ⋮ Central limit theorems for supercritical superprocesses with immigration ⋮ Spines, skeletons and the strong law of large numbers for superdiffusions ⋮ Stable central limit theorems for super Ornstein-Uhlenbeck processes ⋮ Central limit theorems for supercritical superprocesses ⋮ Limit theorems for some critical superprocesses ⋮ Spine decompositions and limit theorems for a class of critical superprocesses

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The prolific backbone for supercritical superprocesses
• Superprocesses and partial differential equations
• \(\mathbb{N}\)-measures for branching exit Markov systems and their applications to differential equations
• Law of large numbers for superdiffusions: the non-ergodic case
• Strong law of large numbers for branching diffusions
• Propriétés de martingales, explosion et représentation de Lévy- Khintchine d'une classe de processus de branchement à valeurs mesures. (Martingale properties, explosions and Levy-Khinchine representation of measure valued branching processes)
• Spectrum of Ornstein-Uhlenbeck operators in \(L ^{p}\) spaces with respect to invariant measures
• Strong law of large numbers for a class of superdiffusions
• Law of large numbers for a class of superdiffusions
• Introductory lectures on fluctuations of Lévy processes with applications.
• CLT for Ornstein-Uhlenbeck branching particle system
• Branching-diffusion processes with no absorbing boundaries. I
• Asymptotic behavior of averaging-processes for a branching process of restricted Brownian particles
• Measure-Valued Branching Markov Processes
• Skew Convolution Semigroups and Related Immigration Processes
• A Spine Approach to Branching Diffusions with Applications to L p -Convergence of Martingales
• Strong limit theorems for general supercritical branching processes with applications to branching diffusions
• Strong limit theorems for supercritical imigration-branching processes.
• Martingale central limit theorems and asymptotic estimation theory for multitype branching processes
• Real Analysis and Probability
• L Log L Criterion for a Class of Superdiffusions
• Limit theorems for multitype continuous time Markov branching processes
• Limit theorems for multitype continuous time Markov branching processes
• A Limit Theorem for Multidimensional Galton-Watson Processes
• Additional Limit Theorems for Indecomposable Multidimensional Galton-Watson Processes
• Some refinements in the theory of supercritical multitype Markov branching processes

This page was built for publication: Central limit theorems for super Ornstein-Uhlenbeck processes