Displaying similar documents to “On the law of large numbers for continuous-time martingales and applications to statistics.”

Representation of continuous associative functions.

Barbara Baccheli (1986)

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.

Decomposition of two parameter martingales.

David Nualart Rodón (1981)

Stochastica

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In this paper we exhibit some decompositions in orthogonal stochastic integrals of two-parameter square integrable martingales adapted to a Brownian sheet which generalize the representation theorem of E. Wong and M. Zakai ([6]). Concretely, a development in a series of multiple stochastic integrals is obtained for such martingales. These results are applied for the characterization of martingales of path independent variation.

Some problems of measure theory which are related to economic theory.

Heinz J. Skala (1982)

Stochastica

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After a short discussion of the first application of measure theoretic tools to economics we show that it is consistent relative to the usual axioms of set theory that there exists no nonatomic probability space of power less than the continuum. This together with other results shows that Aumann's continuum-of-agents methodology provides a sound framework at least for the cooperative theory. There are, however, other problems in economics where, without further assumptions,...

Some remarks on a problem of C. Alsina.

J. Matkowski, M. Sablik (1986)

Stochastica

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Equation [1] f(x+y) + f (f(x)+f(y)) = f (f(x+f(y)) + f(f(x)+y)) has been proposed by C. Alsina in the class of continuous and decreasing involutions of (0,+∞). General solution of [1] is not known yet. Nevertheless we give solutions of the following equations which may be derived from [1]: [2] f(x+1) + f (f(x)+1) = 1, [3] f(2x) + f(2f(x)) = f(2f(x + f(x))). Equation [3] leads to a Cauchy functional equation: ...

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

Manuel de la Sen (1986)

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.

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

J. M. F. Chamayou (1981)

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 < ti ≤ t) Yi c-b(t...

On symmetries and parallelogram spaces.

Mirko Polonijo (1985)

Stochastica

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The notion of a TST-space is introduced and its connection with a parallelogram space is given. The existence of a TST-space is equivalent to the existence of a parallelogram space, which is a new characterization of a parallelogram space. The structure of a TST-space is described in terms of an abelian group.