## Displaying similar documents to “A short note on incremental thermoelasticity.”

### Prediction of time series by statistical learning: general losses and fast rates

Dependence Modeling

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We establish rates of convergences in statistical learning for time series forecasting. Using the PAC-Bayesian approach, slow rates of convergence √ d/n for the Gibbs estimator under the absolute loss were given in a previous work [7], where n is the sample size and d the dimension of the set of predictors. Under the same weak dependence conditions, we extend this result to any convex Lipschitz loss function. We also identify a condition on the parameter space that ensures similar rates...

### A theorem on implication functions defined from triangular norms.

Stochastica

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Several transformation which enable implication functions in multivalued logics to be generated from conjunctions have been proposed in the literature. It is proved that for a rather general class of conjunctions modeled by triangular norms, the generation process is closed, thus shedding some light on the relationships between seemingly independent classes of implication functions.

### Integral equations and time varying linear systems.

Stochastica

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In this paper we study the resolution problem of an integral equation with operator valued kernel. We prove the equivalence between this equation and certain time varying linear operator system. Sufficient conditions for solving the problem and explicit expressions of the solutions are given.

### On the measurement of the activity of a radioactive source and a related stochastic process.

Stochastica

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A method is presented to compute the activity of a radioactive source. The principle of the method is based on the tuning of b, the time constant of the RC circuit of the detector with l being the rate of emission of the source, using a statistical argument. The stochastical process involved refers to the distribution of the following random voltage: Vt = ∑(0 &lt; ti ≤ t) Yi c-b(t...

### On a generalization of sum form functional equation (I).

Stochastica

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The Shannon entropy has the sum form ∑f(p) with f(x) = -x logx (x belonging to [0,1]). This together with the property of additivity leads to the 'sum' functional equation...

Stochastica

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### Representation of continuous associative functions.

Stochastica

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Strengthened forms of Ling's representation theorem concerning a class of continuous associative functions are given: Firstly the monotonicity condition is removed. Then the associativity condition is replaced by the power associativity.

### On the extension of Rosenbrock's theory in algebraic design on multivariable controllers.

Stochastica

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System similarity and system strict equivalence concepts from Rosenbrock's theory on linear systems are used to establish algebraic conditions of model matching as well as an algebraic method for design of centralized compensators. The ideas seem to be extensible without difficulty to a class of decentralized control.

### Dependence of Stock Returns in Bull and Bear Markets

Dependence Modeling

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Despite of its many shortcomings, Pearson’s rho is often used as an association measure for stock returns. A conditional version of Spearman’s rho is suggested as an alternative measure of association. This approach is purely nonparametric and avoids any kind of model misspecification. We derive hypothesis tests for the conditional rank-correlation coefficients particularly arising in bull and bear markets and study their finite-sample performance by Monte Carlo simulation. Further,...