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PDE's for the Dyson, Airy and Sine processes

Mark Adler (2005)

Annales de l’institut Fourier

In 1962, Dyson showed that the spectrum of a $n \times n$ random Hermitian matrix, whose entries (real and imaginary) diffuse according to $n^{2}$ independent Ornstein-Uhlenbeck processes, evolves as $n$ non-colliding Brownian particles held together by a drift term. When $n \to \infty$ , the largest eigenvalue, with time and space properly rescaled, tends to the so-called Airy process, which is a non-markovian continuous stationary process. Similarly the eigenvalues in the bulk, with a different time and space rescaling, tend...

Planar semimartingales obtained by transformations of two-parameter martingales

Minh Duc Nguyen, D. Nualart, M. Sanz (1989)

Séminaire de probabilités de Strasbourg

Poisson Random Fields with Control Measures. I

Ljuban Dedić (2002)

Publications de l'Institut Mathématique

Poisson stochastic integration in Hilbert spaces

Nicolas Privault, Jiang-Lun Wu (1999)

Annales mathématiques Blaise Pascal

Prediction problems [Book]

Nguyen Van Thu (1980)

Probabilistic and analytic formulas for the periodic splines interpolating with multiple nodes

Z. Ciesielski (1979)

Banach Center Publications

Probabilistic cellular automata and random fields with i.i.d. directions

Jean Mairesse, Irène Marcovici (2014)

Annales de l'I.H.P. Probabilités et statistiques

Let us consider the simplest model of one-dimensional probabilistic cellular automata (PCA). The cells are indexed by the integers, the alphabet is ${0, 1}$ , and all the cells evolve synchronously. The new content of a cell is randomly chosen, independently of the others, according to a distribution depending only on the content of the cell itself and of its right neighbor. There are necessary and sufficient conditions on the four parameters of such a PCA to have a Bernoulli product invariant measure....

Probability density for a hyperbolic SPDE with time dependent coefficients

Marta Sanz-Solé, Iván Torrecilla-Tarantino (2007)

ESAIM: Probability and Statistics

We prove the existence and smoothness of density for the solution of a hyperbolic SPDE with free term coefficients depending on time, under hypoelliptic non degeneracy conditions. The result extends those proved in Cattiaux and Mesnager, PTRF123 (2002) 453-483 to an infinite dimensional setting.

Processus gaussiens, markoviens d'ordre p, fortement markoviens d'ordre p et problème de Dirichlet stochastique

Albert Benassi (1979)

Annales de l'I.H.P. Probabilités et statistiques

Proper moving average representations and outer functions in two variables.

Gawarecki, L., Mandrekar, V., Richard, P. (2001)

Georgian Mathematical Journal

Properties of local-nondeterminism of Gaussian and stable random fields and their applications

Yimin Xiao (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

In this survey, we first review various forms of local nondeterminism and sectorial local nondeterminism of Gaussian and stable random fields. Then we give sufficient conditions for Gaussian random fields with stationary increments to be strongly locally nondeterministic (SLND). Finally, we show some applications of SLND in studying sample path properties of $(N, d)$ -Gaussian random fields. The class of random fields to which the results are applicable includes fractional Brownian motion, the Brownian...

Propriétés markoviennes de processus sur R2

Markus Dozzi (1983)

Annales de l'I.H.P. Probabilités et statistiques

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Prediction problems [Book]

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