We consider a random dynamical system in which the state space is an interval, and possible laws of motion are monotone functions. It is shown that if the Markov process generated by this systemâ€¦ (More)

In this review we bring together some results on random dynamical systems and indicate their applications to economics. A random dynamical system is described by a triplet (S, Î“,Q) where S is theâ€¦ (More)

In this article a nonsingular asymptotic distribution is derived for a broad class of underlying distributions on a Riemannian manifold in relation to its curvature. Also, the asymptotic dispersionâ€¦ (More)

A notion of localized splitting is introduced as a further extension of the splitting notions for iterated monotone maps introduced earlier by Dubins and Freedman (1966) and more generally byâ€¦ (More)

We provide an explanation of the main ideas underlying GÃ¶tze's main result in [9] using Stein's method. We also provide detailed derivations of various intermediate estimates. Curiously, we are ledâ€¦ (More)

Iteration of randomly chosen quadratic maps defines a Markov process: Xn+1 = Îµn+1Xn(1 âˆ’ Xn), where Îµn are i.i.d. with values in the parameter space [0, 4] of quadratic maps F Î¸ (x) = Î¸x(1 âˆ’ x). Itsâ€¦ (More)

The records of VLF atmospherics over Calcutta and then over Kalyani (West Bengal) during the torrential rainfall, caused by violent monsoon and post-monsoon depressions, exhibit distinct long-periodâ€¦ (More)

The purpose of this note is to identify an interesting and surprising duality between the equations governing the probability distribution and expected value functional of the stochastic processâ€¦ (More)