Suppose a sequence of random variables {Xn} has negative drift when above a certain threshold and has increments bounded in Lp. When p2 this implies that EXn is bounded above by a constant independent of n and the particular 0sequence {Xn}. When p[less-than-or-equals, slant]2 there are...

We consider a system of particles moving independently on a countable state space, according to a general (non-space-homogeneous) Markov process. Under mild conditions, the number of particles at each site will converge to a product of independent Poisson distributions; this corresponds to...

We consider Markov chains {[Gamma]n} with transitions of the form [Gamma]n=f(Xn,Yn)[Gamma]n-1+g(Xn,Yn), where {Xn} and {Yn} are two independent i.i.d. sequences. For two copies {[Gamma]n} and {[Gamma]n'} of such a chain, it is well known that provided E[log(f(Xn,Yn))]<0, where => is weak convergence. In...</0,>

Bounds on convergence rates for Markov chains are a very widely-studied topic, motivated largely by applications to Markov chain Monte Carlo algorithms. For Markov chains on finite state spaces, previous authors have obtained a number of very useful bounds, including those which involve choices...