Displaying similar documents to “On the Regression of a Random Variable with Respect to a Stochastic Process and, Possibly, p Random Variables”

Random attractors for stochastic two-compartment Gray-Scott equations with a multiplicative noise

Xiaoyao Jia, Juanjuan Gao, Xiaoquan Ding (2016)

Open Mathematics

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In this paper, we consider the existence of a pullback attractor for the random dynamical system generated by stochastic two-compartment Gray-Scott equation for a multiplicative noise with the homogeneous Neumann boundary condition on a bounded domain of space dimension n ≤ 3. We first show that the stochastic Gray-Scott equation generates a random dynamical system by transforming this stochastic equation into a random one. We also show that the existence of a random attractor for the...

On the convergence of the stochastic Galerkin method for random elliptic partial differential equations

Antje Mugler, Hans-Jörg Starkloff (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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In this article we consider elliptic partial differential equations with random coefficients and/or random forcing terms. In the current treatment of such problems by stochastic Galerkin methods it is standard to assume that the random diffusion coefficient is bounded by positive deterministic constants or modeled as lognormal random field. In contrast, we make the significantly weaker assumption that the non-negative random coefficients can be bounded strictly away from zero and infinity...

Generalized RBSDEs with Random Terminal Time and Applications to PDEs

Katarzyna Jańczak-Borkowska (2011)

Bulletin of the Polish Academy of Sciences. Mathematics

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Generalized reflected backward stochastic differential equations have been considered so far only in the case of a deterministic interval. In this paper the existence and uniqueness of solution for generalized reflected backward stochastic differential equations in a convex domain with random terminal time is studied. Applications to the obstacle problem with Neumann boundary conditions for partial differential equations of elliptic type are given.

On gradient-like random dynamical systems

Aya Hmissi, Farida Hmissi, Mohamed Hmissi (2012)

ESAIM: Proceedings

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This paper deals with some characterizations of gradient-like continuous random dynamical systems (RDS). More precisely, we establish an equivalence with the existence of random continuous section or with the existence of continuous and strict Liapunov function. However and contrary to the deterministic case, parallelizable RDS appear as a particular case of gradient-like RDS. The obtained results are generalizations of well-known analogous theorems in the framework of deterministic...

Negative dependence structures through stochastic ordering.

Abdul-Hadi N. Ahmed (1990)

Trabajos de Estadística

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Several new multivariate negative dependence concepts such as negative upper orthant dependent in sequence, negatively associated in sequence, right tail negatively decreasing in sequence and upper (lower) negatively decreasing in sequence through stochastic ordering are introduced. These concepts conform with the basic idea that if a set of random variables is split into two sets, then one is increasing whenever the other is decreasing. Our concepts are easily verifiable and enjoy many...

A determinant formula from random walks

Hery Randriamaro (2023)

Archivum Mathematicum

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One usually studies the random walk model of a cat moving from one room to another in an apartment. Imagine now that the cat also has the possibility to go from one apartment to another by crossing some corridors, or even from one building to another. That yields a new probabilistic model for which each corridor connects the entrance rooms of several apartments. This article computes the determinant of the stochastic matrix associated to such random walks. That new model naturally allows...