5 papers
On beta distributed limits of iterated linear random functions
Shaun McKinlay
We consider several special cases of iterations of random i.i.d. linear functions with beta distributed fixed points that generate nested interval schemes when iterated in a backwa…
On approximation rates for boundary crossing probabilities for the multivariate Brownian motion process
S. McKinlay, K. Borovkov
Motivated by an approximation problem from mathematical finance, we analyse the stability of the boundary crossing probability for the multivariate Brownian motion process, with re…
On explicit form of the stationary distributions for a class of bounded Markov chains
Shaun McKinlay, Konstantin Borovkov
We consider a class of discrete time Markov chains with state space [0,1] and the following dynamics. At each time step, first the direction of the next transition is chosen at ran…
A characterisation of transient random walks on stochastic matrices with Dirichlet distributed limits
Shaun McKinlay
We characterise the class of distributions of random stochastic matrices with the property that the products of i.i.d. copies of converge a.s.…
The Uniform Law for Sojourn Measures of Random Fields
Konstantin Borovkov, Shaun McKinlay
The uniform law for sojourn times of processes with cyclically exchangeable increments is extended to the case of random fields, with general parameter sets, that possess a suitabl…