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We discuss the possibility of applying some standard statistical methods (the least square method, the maximum likelihood method, the method of statistical moments for estimation of parameters) to deterministically chaotic low-dimensional…
Some intriging connections between the properties of nonlinear noise driven systems and the nonlinear dynamics of a particular set of Hamilton's equation are discussed. A large class of Fokker-Planck Equations, like the Schr\"odinger…
Descriptions of complex physical or biological systems often include stochastic contributions, and these are commonly simulated using Wiener processes. In many cases however, non-Gaussian fluctuations may originate from non-Wiener processes…
In this book, we introduce a new approach of sublinear expectation to deal with the problem of probability and distribution model uncertainty. We a new type of (robust) normal distributions and the related central limit theorem under…
A new class of random partial differential equations of parabolic type is considered, where the stochastic term consists of an irregular noisy drift, not necessarily Gaussian, for which a suitable interpretation is provided. After freezing…
This work is devoted to modelling and identification of the dynamics of the inter-sectoral balance of a macroeconomic system. An approach to the problem of specification and identification of a weakly formalized dynamical system is…
Neutrosophic Statistics means statistical analysis of population or sample that has indeterminate (imprecise, ambiguous, vague, incomplete, unknown) data. For example, the population or sample size might not be exactly determinate because…
There are two reasons why uncertainty may not be adequately described by Probability Theory. The first one is due to unique or nearly-unique events, that either never realized or occurred too seldom for frequencies to be reliably measured.…
Statistical inference for a linear stochastic hyperbolic equation with two unknown parameters is studied. Based on observation of coordinates of the solution or their linear combination, minimum contrast estimators are introduced. Strong…
We consider the problem of estimating a smooth functional of an unknown signal with discontinuity from Gaussian observations. The signal is a known function that depends on an unknown parameter. This problem is closely related to the famous…
Uncertainty principle plays a crucial role in quantum mechanics, because it captures the essence of the inevitable randomness associated with the outcomes of two incompatible quantum measurements. Information entropy can perfectly describe…
A new approach for uncertainty management for fuzzy, rule based decision support systems is proposed: The domain expert's knowledge is expressed by a set of rules that frequently refer to vague and uncertain propositions. The certainty of…
In the subjective Bayesian approach uncertainty is described by a prior distribution chosen by the statistician. Fuzzy set theory is another way of representing uncertainty. Here we give a decision theoretic approach which allows a Bayesian…
In order to analyze numerically inverse problems several techniques based on linear and nonlinear stability analysis are presented. These techniques are illustrated on the problem of estimating mobilities and capillary pressure in…
Consider a statistical model with an epistemic restriction such that, unlike in classical mechanics, the allowed distribution of positions is fundamentally restricted by the form of an underlying momentum field. Assume an agent (observer)…
A method to quantify robust performance for situations where structured parameter variations and initial state errors rather than extraneous disturbances are the main performance limiting factors is presented. The approach is based on the…
In stochastic simulation, input uncertainty refers to the output variability arising from the statistical noise in specifying the input models. This uncertainty can be measured by a variance contribution in the output, which, in the…
Generalized Langevin equations with non-linear forces and position-dependent linear friction memory kernels, such as commonly used to describe the effective dynamics of coarse-grained variables in molecular dynamics, are rigorously derived…
The paper considers the problem of estimating the parameters in a continuous time regression model with a non-Gaussian noise of pulse type. The noise is specified by the Ornstein-Uhlenbeck process driven by the mixture of a Brownian motion…
Stochastic parabolic equations are widely used to model many random phenomena in natural sciences, such as the temperature distribution in a noisy medium, the dynamics of a chemical reaction in a noisy environment, or the evolution of the…