In this paper, we will discuss the concept of almost sure convergence for specic groups of fuzzyrandom variables. For this purpose, we use the type of generalized Chebyshev inequalities.Moreover, we show the concept of almost sure convergence of weighted average pairwise NQDof fuzzy random variables.

In this paper, we study the stabilizability of randomly switching linear systems in the presence of finite capacity feedback. Motivated by the structure of communication networks, a stochastic channel was considered that sends words whose size is governed by a random process. Such link is used to transmit state measurements between the plant and the controller. In accordance with previous works...

This paper is concerned with the stability of linear time invariant dynamic systems over the packet erasure channel subject to minimum bit rate constraint when encoder and decoder are unaware of control signal. This assumption results in co-designing encoder, decoder and controller. Encoder, decoder, controller and conditions relating transmission rate to packet erasure probability and eigenval...

We consider the asymptotic almost sure behavior of the solution of the equation u(t, x) = u0(x) + κ ∫ t

We study the almost sure convergence of the Bartlett estimator for the asymptotic variance of the sample mean of a stationary weekly dependent process. We also study the a. s. behavior of this estimator in the case of long-range dependent observations. In the weakly dependent case, we establish conditions under which the estimator is strongly consistent. We also show that, after appropriate nor...

Two-dimensional (2-D) and, more generally, multidimensional harmonic retrieval is of interest in a variety of applications, including transmitter localization and joint time and frequency offset estimation in wireless communications. The associated identifiability problem is key in understanding the fundamental limitations of parametric methods in terms of the number of harmonics that can be re...

I would like to tell you about an easily stated problem which lies at the border of geometry, probability and classical analysis. In the summer of 2005 two undergraduates at McGill University worked in this general area, and were able to make some progress. When posing the project to them I made a certain conjecture, and (as expected) they did not get far enough in their eight week project to b...

We consider a financial model with permanent price impact. Continuous time trading dynamics are derived as the limit of discrete rebalancing policies. We then study the problem of super-hedging a European option. Our main result is the derivation of a quasi-linear pricing equation. It holds in the sense of viscosity solutions. When it admits a smooth solution, it provides a perfect hedging stra...

This paper considers the computational hardness of computing expected outcomes and deciding (universal) (positive) almost–sure termination of probabilistic programs. It is shown that computing lower and upper bounds of expected outcomes is Σ 1– and Σ 0 2–complete, respectively. Deciding (universal) almost–sure termination as well as deciding whether the expected outcome of a program equals a gi...

We consider the asymptotic almost sure behavior of the solution of the equation u(t, x) = u0(x) + κ ∫ t