Arcsine and Darling–Kac laws for piecewise linear random interval maps

Laws of Large Numbers for Random Linear

The computational solution of large scale linear programming problems contains various difficulties. One of the difficulties is to ensure numerical stability. There is another difficulty of a different nature, namely the original data, contains errors as well. In this paper, we show that the effect of the random errors in the original data has a diminishing tendency for the optimal value as the...

Arcsine Laws and Interval Partitions Derived from a Stable Subordinator

Le"vy discovered that the fraction of time a standard one-dimensional Brownian motion B spends positive before time t has arcsine distribution, both for / a fixed time when B, # 0 almost surely, and for / an inverse local time, when B, = 0 almost surely. This identity in distribution is extended from the fraction of time spent positive to a large collection of functionals derived from the lengt...

Dynamics of piecewise linear interval maps with hysteresis

We study a special case of multistate maps, piecewise linear interval maps with hysteresis. The main object of study is the global attractor. We ® nd the conditions for it to be lower semicontinuous. We also prove that it coincides with the non-wander ing set and prove several facts about omega-limit sets of the discontinuity points of the map. 1 General introduction The present paper deals wit...

Ulam's method for random interval maps

We consider the approximation of absolutely continuous invariant measures (ACIMs) of systems defined by random compositions of piecewise monotonic transformations. Convergence of Ulam’s finite approximation scheme in the case of a single transformation was dealt with by Li (1976 J. Approx. Theory 17 177–86). We extend Ulam’s construction to the situation where a family of piecewise monotonic tr...

Random linear maps