In this paper, we investigate specific least action principles for laws of stochastic processes within a framework which stands on filtrations preserving variations. The associated Euler–Lagrange conditions, obtain, exhibit deterministic process in the dynamics aside canonical martingale term. particular, taking functionals, extremal with respect to those variations encompass continuous semi-ma...

Reaching agreement despite noise in communication is a fundamental problem multi-agent systems. Here we study this under an idealized model, where it assumed that agents can sense the general tendency system. More specifically, consider $n$ agents, each being associated with real-valued number. In round, agent receives noisy measurement of average value, and then updates its which turn perturbe...

We study a particular class of moving average processes which possess a property called localisability. This means that, at any given point, they admit a “tangent process”, in a suitable sense. We give general conditions on the kernel g defining the moving average which ensures that the process is localisable and we characterize the nature of the associated tangent processes. Examples include t...

2 Moving average models Definition. The moving average model of order q, or MA(q), is defined to be Xt = t + θ1 t−1 + θ2 t−2 + · · ·+ θq t−q, where t i.i.d. ∼ N(0, σ). Remarks: 1. Without loss of generality, we assume the mean of the process to be zero. 2. Here θ1, . . . , θq (θq 6= 0) are the parameters of the model. 3. Sometimes it suffices to assume that t ∼WN(0, σ). Here we assume normality...

The harmonizable Piranashvili–type stochastic processes are approximated by finite time shifted average sampling sums. Explicit truncation error upper bounds are established. Various corollaries and special cases are discussed. Submitted: May 7, 2014 Address correspondence to Tibor Pogány, Faculty of Maritime Studies, University of Rijeka, Studentska 2, HR-51000 Rijeka, Croatia; E-mail: poganj@...

We investigate the average characteristic polynomial E [∏N i=1(z−xi) ] where the xi’s are real random variables drawn from a Biorthogonal Ensemble, i.e. a determinantal point process associated with a bounded finite-rank projection operator. For a subclass of Biorthogonal Ensembles, which contains Orthogonal Polynomial Ensembles and (mixed-type) Multiple Orthogonal Polynomial Ensembles, we prov...

We consider the problem of reconstructing a wide sense stationary band-limited process from its local averages taken either at the Nyquist rate or above. As a result, we obtain a sufficient condition under which average sampling expansions hold in mean square and for almost all sample functions. Truncation and aliasing errors of the expansion are also discussed.

Formal analysis of decentralized decision making has become a thriving research area in recent years, producing a number of multi-agent extensions of Markov decision processes. While much of the work has focused on optimizing discounted cumulative reward, optimizing average reward is sometimes a more suitable criterion. We formalize a class of such problems and analyze its characteristics, show...

^ The Semi-Markov Decision model is considered under the criterion of long-run average cost. A new criterion, which for any policy considers the limit of the expected cost Incurred during the first n transitions divided by the expected length of the first n transitions, is considered. Conditions guaranteeing that an optimal stationary (nonrandomized) policy exist are then presented. It is also ...