Journal ArticleDOI
On isotropic brownian motions
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In this paper, a detailed study of isotropic brownian motion on matrices and brownian flows associated with isotropics gaussian fields is presented, including characteristic exponents, stability, asymptotic behaviour, statistical equilibrium and statistical equilibrium.Abstract:
This paper includes a detailed study of isotropic brownian motion on matrices and brownian flows associated with isotropic gaussian fields. Characteristic exponents, stability, asymptotic behaviour, statistical equilibrium are the topics on which the main results are obtained.read more
Citations
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On the Diffusion of Shape
TL;DR: In this article, the authors study the global geometric properties of a manifold embedded in Euclidean space, as it evolves under a stochastic flow of diffeomorphisms.
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Statistical models for spatial patterns of heavy particles in turbulence
TL;DR: The dynamics of heavy particles suspended in turbulent flows is of fundamental importance for a wide range of questions in astrophysics, atmospheric physics, oceanography, and technology as discussed by the authors, and it is known that heavy particles respond in intricate ways to turbulent fluctuations of the carrying fluid: noninteracting particles may cluster together and form spatial patterns even though the fluid is incompressible.
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Flows, coalescence and noise
Yves Le Jan,Olivier Raimond +1 more
TL;DR: In this paper, a stochastic differential equation (SDE) is used to describe stationary "fluid" random evolutions with independent increments, and it is shown that all solutions of the SDE can be obtained by filtering a coalescing motion with respect to a subnoise containing the Gaussian part of its noise.
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Integration of Brownian vector fields
Yves Le Jan,Olivier Raimond +1 more
TL;DR: Using the Wiener chaos decomposition, the authors showed that strong solutions of non-Lipschitzian stochastic differential equations are given by random Markovian kernels.
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Entropy Formula for Random Transformations
F. Ledrappier,Lai Sang Young +1 more
TL;DR: In this paper, random strange attractors with random Sinai-Bowen-Ruelle measures for the composition of independent random diffeomorphisms are presented. But they are not suitable for deterministic deterministic systems.
References
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Book
Stochastic differential equations and diffusion processes
TL;DR: In this article, Stochastic Differential Equations and Diffusion Processes are used to model the diffusion process in stochastic differential equations. But they do not consider the nonlinearity of diffusion processes.
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Stochastic differential equations and diffusion processes: Nobuyuki Ikeda and Shinzo Watanabe North-Holland, Amsterdam, 1981, xiv + 464 pages, Dfl.175.00
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Foundations of the theory of algebraic invariants
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Flows of stochastic dynamical systems: ergodic theory
TL;DR: In this paper, a version of the multiplicative ergodic (Oseledec) theorem for the flow of a nonlinear stochastic system defined on a smooth compact manifold is presented.