Biggins, J.D. (2008) The growth of iterates of multivariate generating functions. Transactions of the American Mathematical Society (TRAN), 360. pp. 4305-4334. ISSN 0002-9947
The vector-valued function of a -vector has components . For each , is the (multivariate) Laplace transform of a discrete measure concentrated on with only a finite number of atoms. The main objective is to give conditions for the functional iterates of to grow like for a suitable . The initial stimulus was provided by results of Miller and O'Sullivan (1992) on enumeration issues in `context free languages', results which can be improved using the theory developed here. The theory also allows certain results in Jones (2004) on multitype branching to be proved under significantly weaker conditions.
|Institution:||The University of Sheffield|
|Academic Units:||The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield)|
|Depositing User:||Mrs Megan Hobbs|
|Date Deposited:||29 Mar 2010 14:12|
|Last Modified:||16 Nov 2015 11:48|
|Publisher:||American Mathematical Society|