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Stochastic Modulation Equations on Unbounded Domains

Bianchi, Luigi A., Blömker, Dirk (2017)

Proceedings of Equadiff 14

We study the impact of small additive space-time white noise on nonlinear stochastic partial differential equations (SPDEs) on unbounded domains close to a bifurcation, where an infinite band of eigenvalues changes stability due to the unboundedness of the underlying domain. Thus we expect not only a slow motion in time, but also a slow spatial modulation of the dominant modes, and we rely on the approximation via modulation or amplitude equations, which acts as a replacement for the lack of random...

Stochastic ordering of random kth record values

Wiesław Dziubdziela, Agata Tomicka-Stisz (1999)

Applicationes Mathematicae

Let X 1 , X 2 , . . . be a sequence of independent and identically distributed random variables with continuous distribution function F(x). Denote by X(1,k),X(2,k),... the kth record values corresponding to X 1 , X 2 , . . . We obtain some stochastic comparison results involving the random kth record values X(N,k), where N is a positive integer-valued random variable which is independent of the X i .

Stochastic Poisson-Sigma model

Rémi Léandre (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We produce a stochastic regularization of the Poisson-Sigma model of Cattaneo-Felder, which is an analogue regularization of Klauder’s stochastic regularization of the hamiltonian path integral [23] in field theory. We perform also semi-classical limits.

Stochastic process measurability conditions

J. L. Doob (1975)

Annales de l'institut Fourier

If the separability of the separable process definition is replaced by a set of optional (predictable) times, a new property is obtained, optional (predictable) separability. A well measurable (accessible) process is necessarily optionally (predictably) separable. Proofs of limit properties of a separable process become proofs of the same limit properties of a well measurable (predictable) process.

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