A hybrid quantum-classical filtering problem, where a qubit system is disturbed by a classical stochastic process, is investigated. The strategy is to model the classical disturbance by using an ...optical cavity. The relations between classical disturbances and the cavity analog system are analyzed. The dynamics of the enlarged quantum network system, which includes a qubit system and a cavity system, are derived. A stochastic master equation for the qubit-cavity hybrid system is given, based on which estimates for the state of the cavity system and the classical signal are obtained. The quantum-extended Kalman filter is employed to achieve efficient computation. The numerical results are presented to illustrate the effectiveness of our methods.
Regression analysis is a huge part of mathematical and applied statistics. Nonlinear regression analysis is a significant extension and complication of classical linear regression analysis, due to ...the use of nonlinear or partially nonlinear in parameters models that describe more adequately than linear model phenomena requiring statistical analysis. A large number of applied problems in the numerical scientific, technical, and humanitarian fields of knowledge give impetus to the development of nonlinear regression analysis. The task of estimation the vector signal parameter in the «signal + noise» observation models is a well-known problem of statistics of stochastic processes, and in the case of a nonlinear signal parameter is the problem of nonlinear regression analysis. Among the variety of nonlinear regression analysis problems the problem of estimating amplitudes and angular frequencies of the sum of harmonic oscillations that are observed against the background of a random noise, takes significant place due to its numerous applications. Statistical model of such a type is said to be trigonometric regression, and the problem of statistical estimation is called the problem of detecting hidden periodicities. The paper is devoted to the study of time continuous trigonometric regression model where the random noise is a linear L´evy driven stationary of the fourth order stochastic process with zero mean, integrable and square integrable impulse transmission function. This assumption leads to the integrability of the noise covariance function and cumulant function of the fourth order. To estimate unknown amplitudes and angular frequencies of such a trigonometric model we use the least squares estimators in the Walker sense, that is special parametric set are considered to distinguish properly different angular frequencies in the sum of harmonic oscillations. Theorem on strong consistency of the least squares estimators is proved in the paper under the assumption on the random noise described above. To obtain such a result a very important lemma was proved on the uniform tending to zero almost surely of the average value of L´evy-driven linear stochastic process Fourier transform. This Lemma is the main tool of the strong consistency Theorem proof. To prove the Theorem we, firstly, find some expressions for the least squares estimates of amplitudes via corresponding estimates of angular frequencies. Secondly, we substitute these formulas into the functional of the least squares method. The last step of the proof consists of the L2- norm transformation of the difference between empirical trigonometric regression function and true regression function such that this norm tends to zero almost surely if and on if the estimators are strongly consistent.
For dynamical systems that can be modelled as asymptotically stable linear systems forced by Gaussian noise, this paper develops methods to infer (estimate) their dominant modes from observations in ...real time. The modes can be real or complex. For a real mode (monotone decay), the goal is to infer its damping rate and mode shape. For a complex mode (oscillatory decay), the goal is to infer its frequency, damping rate and (complex) mode shape. Their amplitudes and correlations are encoded in a mode covariance matrix that is also to be inferred. The work is motivated and illustrated by the problem of detection of oscillations in power flow in AC electrical networks. Suggestions of some other applications are given.
We demonstrate that “an arrow of time” that is being determined by the joint distributions of successive process variables, or equivalently a break of temporal symmetry (i.e. a symmetry/asymmetry ...dichotomy), can be evidenced solely on probabilistic grounds, on the basis of structural dependencies and statistical attributes of observed quantities, without the intervention of any symmetric or asymmetric physical laws. We do so for the simplest case of stable Markovian recursions, and show that a break of temporal symmetry can occur as the combined effect of lack of Gaussianity and statistical dependencies, even in the case when the increments of the generated process are independent and identically distributed with symmetric marginal. This striking result occurs under conditions of stationarity, without any changes in the dynamic recursion equation of the process, allowing for statistical characterization of temporal symmetries versus asymmetries. To that end, we introduce and exemplify the use of an estimator based on fractional low-order joint moments, which exists for all stationary stochastic processes with strictly stable symmetric marginals, and can be used to parameterize their dependence structure in a linear setting.
A bi-parametric family of non-linear stochastic processes is introduced, to investigate the properties of second-order random processes with a narrow-band spectrum in the mechanics of the sea waves. ...In particular, the expressions of the probability density function and of the probabilities of exceedance of the absolute maximum and absolute minimum are obtained for this stochastic family. The analytical results are particularized for some processes of basic interest in the mechanics of the sea waves: the free surface displacement, and the fluctuating wave pressure beneath the sea surface.
We survey a number of important results concerning aggregation of dynamic, stochastic relations. We do not aim at a comprehensive review; instead, we focus heavily on the results collected in Forni ...and Lippi Forni, M., Lippi, M., 1997. Aggregation and the Microfoundations of Dynamic Macroeconomics. Oxford University Press, Oxford. We argue that the representative-agent assumption is misleading and the microfoundation of dynamic macroeconomics should be based on explicit modeling of heterogeneity across agents. An unpleasant aspect of this modeling strategy is that macroeconomic implications of micro theory are difficult to obtain. However, difficulties are reduced by large number results. Moreover, puzzling implications of existing theories could be reconciled with empirical evidence on macro data.
The definition of a random periodic process, the main properties of the process, and a characteristic function for a process of general type that allows us to scope the random periodic process are ...proposed. Modelling of a linear stochastic process is used as an example for a practical application of a periodic white noise. The characteristic function of nonstationary linear stochastic processes is presented.
White noise in information signal models Zvaritch, V.; Mislovitch, M.; Martchenko, B.
Applied mathematics letters,
05/1994, Letnik:
7, Številka:
3
Journal Article
Recenzirano
Odprti dostop
A definition of white noise processes in strong sense, main properties of the noise, a characteristic function for a white noise of general type that allows us to characterize the white noise ...processes are suggested. Modeling of a linear stochastic process is used as an example of the practical application of the white noise in the strong sense.
In a recent paper R. Dudley gave a characterization of those sequences of independent and identically distributed random variables which are $l_p$-compatible for $p \geqq 1$. In the present note we ...extend his result into $p \in (0, 1 \rbrack$ and provide some conditions (necessary or sufficient) for $l_\varphi$-compatibility of a sequence of independent random variables not necessarily identically distributed.
Traffic noise, microscale air pollution and other adverse environmental impacts of highways can often be represented as the superposition of the impacts of the individual vehicles. A Markov renewal ...process is often a useful representation of vehicle positions in multi-type "follow-the-leader," traffic flow. The impact of the vehicles is thus a filtered Markov renewal process whose moments can be calculated recursively using the method of L. Takacs and W. K. Smith.
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