About: Asymptotics of maxima of (2,1) and (1,2) random walks with asymptotically zero drifts and product of nonnegative 2-by-2 matrices

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About: Asymptotics of maxima of (2,1) and (1,2) random walks with asymptotically zero drifts and product of nonnegative 2-by-2 matrices Goto Sponge NotDistinct Permalink

An Entity of Type : schema:ScholarlyArticle, within Data Space : wasabi.inria.fr associated with source document(s)

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type	Academic Article research paper schema:ScholarlyArticle
isDefinedBy	Covid-on-the-Web dataset
has title	Asymptotics of maxima of (2,1) and (1,2) random walks with asymptotically zero drifts and product of nonnegative 2-by-2 matrices
Creator	Sun, Hongyan Wang, Hua-Ming
Source	ArXiv
abstract	Consider (2,1) and (1,2) random walks with asymptotically zero drifts. Let $M$ be the maximum of an excursion starting from $2$ and ending at some point below $2.$ We study the distribution of $M$ and characterize its asymptotics, which are quite different from the ones of simple random walks. Our methods are based on the asymptotics of product of 2-by-2 nonnegative matrices and continued fractions. So, we also get a limit theorem of the product of nonnegative 2-by-2 matrices which has its own interest. Let $A_kA_{k-1}/cdots A_1$ be the product of some nonnegative 2-by-2 matrices. Under certain conditions, we show that $/forall i,j= 1,2,$ $(A_kA_{k-1}/cdots A_1)_{i,j}/sim c/varrho(A_k)/varrho(A_{k-1})/cdots /varrho(A_1)$ as $k/rightarrow/infty,$ where $/varrho(A_n)$ is the spectral radius of $A_n$ and $c/in(0,/infty)$ is some constant.
has issue date	2020-04-28(xsd:dateTime)
has license	arxiv
sha1sum (hex)	4acfc87d7807c6f99044decba2e081a904d77eda
resource representing a document's title	Asymptotics of maxima of (2,1) and (1,2) random walks with asymptotically zero drifts and product of nonnegative 2-by-2 matrices
resource representing a document's body	covid:4acfc87d7807c6f99044decba2e081a904d77eda#body_text
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