Self-similar scaling limits of Markov chains on the positive integers
نویسندگان
چکیده
منابع مشابه
Self-similar scaling limits of non-increasing Markov chains
We study scaling limits of non-increasing Markov chains with values in the set of non-negative integers, under the assumption that the large jump events are rare and happen at rates that behave like a negative power of the current state. We show that the chain starting from n and appropriately rescaled, converges in distribution, as n → ∞, to a non-increasing self-similar Markov process. This c...
متن کاملSelf-similar branching Markov chains
The main purpose of this work is to study self-similar branching Markov chains. First we will construct such a process. Then we will establish certain Limit Theorems using the theory of self-similar Markov processes.
متن کاملOn the future infimum of positive self-similar Markov processes
On the future infimum of positive self-similar Markov processes. Abstract We establish integral tests and laws of the iterated logarithm for the upper envelope of the future infimum of positive self-similar Markov processes and for increasing self-similar Markov processes at 0 and +∞. Our proofs are based on the Lamperti representation and time reversal arguments due to Chaumont and Pardo [9]. ...
متن کاملSimilar Markov Chains
In a recent paper, Lenin et al. [10] introduced the idea of similarity in the context of birth-death processes. The present note examines the extent to which their results can be extended to arbitrary Markov chains. We prove, under a variety of conditions, that similar chains are strongly similar in a sense which we shall describe, and we prove that minimal chains are strongly similar if and on...
متن کاملThe upper envelope of positive self-similar Markov processes
We establish integral tests and laws of the iterated logarithm at 0 and at +∞, for the upper envelope of positive self-similar Markov processes. Our arguments are based on the Lamperti representation, time reversal arguments and on the study of the upper envelope of their future infimum due to Pardo [19]. These results extend integral test and laws of the iterated logarithm for Bessel processes...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Applied Probability
سال: 2016
ISSN: 1050-5164
DOI: 10.1214/15-aap1157