In a recent work (Bhatt et al., SIAM J. Control Optim. 39 (2000) 928) various Markov and ergodicity properties of the nonlinear filter, for the classical model of nonlinear filtering, were studied. It was shown that under quite general conditions, when the signal is a Feller-Markov process with...

Large deviation principles are established for the Fleming-Viot process with neutral mutation and with selection, and the associated equilibrium measures as the sampling rate approaches zero and when the state space is equipped with the weak topology. The path-level large deviation results...

The closure property of the up-shifted likelihood ratio order under convolutions was first proved by Shanthikumar and Yao (Stochastic Process. Appl. 23 (1986) 259) by establishing a stochastic monotonicity property of birth-death processes. Lillo et al. (Recent Advances in Reliability Theory:...

We consider algorithms for simulation of iterated Itô integrals with application to simulation of stochastic differential equations. The fact that the iterated Itô integralconditioned on Wi(tn+h)-Wi(tn) and Wj(tn+h)-Wj(tn), has an infinitely divisible distribution utilised for the simultaneous...

We find necessary and sufficient conditions for the CLT for Markov chains with a countable state space embedded in the space lp for p[greater-or-equal, slanted]1. This result is an extension of the uniform CLT over the family of indicator functions in Levental (Stochastic Processes Appl. 34...

In this paper, we establish a small time large deviation principle for diffusion processes on configuration spaces.

Let [Phi]z be the uncovered set (i.e., the complement of the union of intervals) at time z in the one-dimensional Johnson-Mehl model. We derive a bound for the total variation distance between the distribution of the number of components of [Phi]z[intersection](0,t] and a compound...

Let (A1,B1,L1),(A2,B2,L2),... be a sequence of independent and identically distributed random vectors. For , denoteYn=B1+A1B2+A1A2B3+...+A1...An-1Bn+A1...AnLn.For M0, define the time of ruin by TM=inf{n YnM} (TM=+[infinity], if Yn[less-than-or-equals, slant]M for n=1,2,...). We are interested in...

A classical damping Hamiltonian system perturbed by a random force is considered. The locally uniform large deviation principle of Donsker and Varadhan is established for its occupation empirical measures for large time, under the condition, roughly speaking, that the force driven by the...

Let (Xi) be a martingale difference sequence and Sn=[summation operator]i=1n Xi. We prove that if supi E(eXi)<[infinity] then there exists c>0 such that [mu](Snn)[less-than-or-equals, slant]e-cn1/3; this bound is optimal for the class of martingale difference sequences which are also strictly stationary and ergodic. If the...</[infinity]>