Search results for "stochastic"
showing 10 items of 1018 documents
Stochastic factorizations, sandwiched simplices and the topology of the space of explanations
2003
We study the space of stochastic factorizations of a stochastic matrix V, motivated by the statistical problem of hidden random variables. We show that this space is homeomorphic to the space of simplices sandwiched between two nested convex polyhedra, and use this geometrical model to gain some insight into its structure and topology. We prove theorems describing its homotopy type, and, in the case where the rank of V is 2, we give a complete description, including bounds on the number of connected components, and examples in which these bounds are attained. We attempt to make the notions of topology accessible and relevant to statisticians.
Relations between structure and estimators in networks of dynamical systems
2011
The article main focus is on the identification of a graphical model from time series data associated with different interconnected entities. The time series are modeled as realizations of stochastic processes (representing nodes of a graph) linked together via transfer functions (representing the edges of the graph). Both the cases of non-causal and causal links are considered. By using only the measurements of the node outputs and without assuming any prior knowledge of the network topology, a method is provided to estimate the graph connectivity. In particular, it is proven that the method determines links to be present only between a node and its “kins”, where kins of a node consist of …
Robust stabilisation of 2D state-delayed stochastic systems with randomly occurring uncertainties and nonlinearities
2013
This paper is concerned with the state feedback control problem for a class of two-dimensional (2D) discrete-time stochastic systems with time-delays, randomly occurring uncertainties and nonlinearities. Both the sector-like nonlinearities and the norm-bounded uncertainties enter into the system in random ways, and such randomly occurring uncertainties and nonlinearities obey certain mutually uncorrelated Bernoulli random binary distribution laws. Sufficient computationally tractable linear matrix inequality–based conditions are established for the 2D nonlinear stochastic time-delay systems to be asymptotically stable in the mean-square sense, and then the explicit expression of the desired…
On Fuzzy Stochastic Integral Equations—A Martingale Problem Approach
2011
In the paper we consider fuzzy stochastic integral equations using the methods of stochastic inclusions. The idea is to consider an associated martingale problem and its solutions in order to obtain a solution to the fuzzy stochastic equation.
Martingale Convergence Theorems and Their Applications
2020
We became familiar with martingales X=(X n ) n∈N0 as fair games and found that under certain transformations (optional stopping, discrete stochastic integral) martingales turn into martingales. In this chapter, we will see that under weak conditions (non-negativity or uniform integrability) martingales converge almost surely. Furthermore, the martingale structure implies L p -convergence under assumptions that are (formally) weaker than those of Chapter 7. The basic ideas of this chapter are Doob’s inequality (Theorem 11.4) and the upcrossing inequality (Lemma 11.3).
Influence of the quadratic term in the alongwind stochastic response of SDOF structures
1996
A parametric study, regarding the influence of the quadratic pressure term, which is often neglected in the literature, on the stochastic alongwind response of a single-degree-of-freedom (SDOF) structure subjected to wind action, is presented. The results are reported in terms of percentages of difference in the evaluation of the response, by considering and neglecting the quadratic pressure term. The changing parameters considered are: the terrain drag coefficient, the structure height, the structure natural radian frequency, the structure damping coefficient and the wind reference mean velocity. The response stochastic analysis has been carried out in the time domain, by means of the mome…
A Branch-and-Cut method for the Capacitated Location-Routing Problem
2011
International audience; Recent researches in the design of logistic networks have shown that the overall distribution cost may be excessive if routing decisions are ignored when locating depots. The Location-Routing Problem (LRP) overcomes this drawback by simultaneously tackling location and routing decisions. The aim of this paper is to propose an exact approach based on a Branch-and-Cut algorithm for solving the LRP with capacity constraints on depots and vehicles. The proposed method is based on a zero-one linear model strengthened by new families of valid inequalities. The computational evaluation on three sets of instances (34 instances in total), with 5–10 potential depots and 20–88 …
Mode-superposition correction method for deterministic and stochastic analysis of structural systems
2001
The role played by the modal analysis in the framework of structural dynamics is fundamental from both deterministic and stochastic point of view. However the accuracy obtained by means of the classical modal analysis is not always satisfactory. Therefore it is clear the importance of methods able to correct the modal response in such a way to obtain the required accuracy. Many methods have been proposed in the last years but they are meaningful only when the forcing function is expressed by an analytical function. Moreover in stochastic analysis they fail for white noise excitation. In the paper a method able to give a very accurate response for both deterministic and stochastic input is p…
A perturbation approach for the response of dynamically modified structural systems
1998
The problem of the structural analysis under changes of dynamical parameters is of particular interest. This is due to the fact that often the real structures are different from the predicted ones. In this paper, an unconditionally stable step-by-step procedure, able to evaluate the deterministic response of linear structures with modifications, is presented. The proposed procedure requires the evaluation of the transition matrix, which is the fundamental operator of the step-by-step solution, by means of a perturbation approach. This technique overcomes the difficulties connected with the evaluation of the eigenproperties of the modified structures usually required to obtain the transition…
Attractors of stochastic lattice dynamical systems with a multiplicative noise and non-Lipschitz nonlinearities
2012
AbstractIn this paper we study the asymptotic behavior of solutions of a first-order stochastic lattice dynamical system with a multiplicative noise.We do not assume any Lipschitz condition on the nonlinear term, just a continuity assumption together with growth and dissipative conditions, so that uniqueness of the Cauchy problem fails to be true.Using the theory of multi-valued random dynamical systems we prove the existence of a random compact global attractor.