On the attracting orbit of a nonlinear transformation arising from renormalization of hierarchically interacting diffusions. II: The non-compact case
Motivated from the study of the space-time scaling limit of certain infinite system of interacting diffusion, this paper analyzes the \(n\)-fold composition of nonlinear integral operator acting on a class of functions on \([0,\infty)\). In part I [Can. J. Math. 47, No. 1, 3-27 (1995; Zbl 0832.60097)], the compact space \([0, 1]\) was treated. However, the non-compact case exhibits different behavior. The attracting orbits and attracting fixed points of the \(n\)-fold operator are identified and several convergences of the \(n\)-fold operator to the orbits or fixed points are characterized. For which, the authors present seven theorems, their proofs are analytic but rather technical and lengthy as one can imagine. However, the probabilistic meaning of the results are carefully explained.
scientific article; zbMATH DE number 1013818