In this paper, we study asymptotic stability properties of risk-sensitive filters with respect to their initial conditions. In particular, we consider a linear time-invariant systems with initial conditions that are not necessarily Gaussian. We show that in the case of Gaussian initial conditions, the optimal risksensitive filter asymptotically converges to any suboptimal filter initialized wit...

Completion of the proof of Theorem 1. Step 6: To show (6.5), which gives the Radon–Nikodym derivative of the restriction of the distribution of X(i) − x to a small ball about the origin Recall that Bδ(u) = {y ∈ Rd : ‖y − u‖ ≤ δ}, and that νd denotes ddimensional Lebesgue measure. For a Borel subset A of Rd, let N(A) = ∑n i=1 1{Xi∈A}. It follows from the hypothesis (A.2) that for x ∈ S n with n ...

Let W be the number of points in (0, t] of a stationary finitestate Markov renewal point process. We derive a bound for the total variation distance between the distribution of W and a compound Poisson distribution. For any nonnegative random variable ζ, we construct a “strong memoryless time” ζ̂ such that ζ − t is exponentially distributed conditional on {ζ̂ ≤ t, ζ > t}, for each t. This is used...

The paper starts with an appropriate version of the bounded distortion theorem. We show that for a regular, satisfying the "Open Set Condition", iterated function system of countably many conformal contractions of an open connected subset of a Euclidean space IR d with d 3, the Radon-Nikodym derivative dd=dm has a real-analytic extension on an open neighbourhood of the limit set of this system,...

The main purpose of this paper is to prove some results of uniform boundedness principle type without the use of Baire’s category theorem in certain topological vector spaces; this provides an alternate route and important technique to establish certain basic results of functional analysis. As applications, among other results, versions of the Banach-Steinhaus theorem and the Nikodym boundednes...

A Boolean algebra has the Nikodym property if every pointwise bounded sequence of finitely additive measures on is uniformly bounded. Assuming Diamond Principle ◇, we will construct an example a minimally generated with property. The Stone space such must necessarily be Efimov space. converse is, however, not true—again under ◇ provide whose but which does have results interesting measure-theor...