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Quadratic estimation from non-independent uncertain observations with coloured noise.

S. Nakamori, R. Caballero, A. Hermoso, J. Jiménez, J. Linares (2004)

Extracta Mathematicae

Recursive least-squares quadratic filtering and fixed-point smoothing algorithms for signal estimation from uncertain observations are derived when the uncertainty is modeled by not necessarily independent variables and the observations contain white plus coloured noise. The proposed estimators do not require the knowledge of the state-space of the model generating the signal, but only the moments, up to the fourth one, of the processes involved, along with the probability that the signal exists...

Quantile hedging on markets with proportional transaction costs

Michał Baran (2003)

Applicationes Mathematicae

The problem of risk measures in a discrete-time market model with transaction costs is studied. Strategy effectiveness and shortfall risk are introduced. This gives a generalization of quantile hedging presented in [4].

Quantitative recurrence in two-dimensional extended processes

Françoise Pène, Benoît Saussol (2009)

Annales de l'I.H.P. Probabilités et statistiques

Under some mild condition, a random walk in the plane is recurrent. In particular each trajectory is dense, and a natural question is how much time one needs to approach a given small neighbourhood of the origin. We address this question in the case of some extended dynamical systems similar to planar random walks, including ℤ2-extension of mixing subshifts of finite type. We define a pointwise recurrence rate and relate it to the dimension of the process, and establish a result of convergence in...

Quantized distributed output regulation of multi-agent systems

Xiaoli Wang, Yumin Chen (2016)

Kybernetika

Motivated by digital communication channel, we consider the distributed output regulation problem for linear multi-agent systems with quantized state measurements. Quantizers take finitely many values and have an adjustable "zoom" parameter. Quantized distributed output regulation concerns designing distributed feedback by employing quantized technique for multi-agent systems such that all agents can track an active leader, and/or distributed disturbance rejection. With the solvability conditions...

Quasi-diffusion solution of a stochastic differential equation

Agnieszka Plucińska, Wojciech Szymański (2007)

Applicationes Mathematicae

We consider the stochastic differential equation X t = X ₀ + ∫ 0 t ( A s + B s X s ) d s + ∫ 0 t C s d Y s , where A t , B t , C t are nonrandom continuous functions of t, X₀ is an initial random variable, Y = ( Y t , t ≥ 0 ) is a Gaussian process and X₀, Y are independent. We give the form of the solution ( X t ) to (0.1) and then basing on the results of Plucińska [Teor. Veroyatnost. i Primenen. 25 (1980)] we prove that ( X t ) is a quasi-diffusion proces.

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