Gibbs-Cox Random Fields and Burgers Turbulence
We study the large time behavior of random fields which are solutions of a nonlinear partial differential equation, called Burgers' equation, under stochastic initial conditions. These are assumed to be of the shot noise type with the Gibbs-Cox process driving the spatial distribution of the &q...
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| Veröffentlicht in: | The Annals of applied probability 1995-05, Vol.5 (2), p.461-492 |
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| container_title | The Annals of applied probability |
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| creator | Funaki, T. Surgailis, D. Woyczynski, W. A. |
| description | We study the large time behavior of random fields which are solutions of a nonlinear partial differential equation, called Burgers' equation, under stochastic initial conditions. These are assumed to be of the shot noise type with the Gibbs-Cox process driving the spatial distribution of the "bumps." In certain cases, this work extends an earlier effort by Surgailis and Woyczynski, where only noninteracting "bumps" driven by the traditional doubly stochastic Poisson process were considered. In contrast to the previous work by Bulinski and Molchanov, a non-Gaussian scaling limit of the statistical solutions is discovered. Burgers' equation is known to describe various physical phenomena such as nonlinear and shock waves, distribution of self-gravitating matter in the universe and so forth. |
| doi_str_mv | 10.1214/aoap/1177004774 |
| format | Article |
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A.</creator><creatorcontrib>Funaki, T. ; Surgailis, D. ; Woyczynski, W. A.</creatorcontrib><description>We study the large time behavior of random fields which are solutions of a nonlinear partial differential equation, called Burgers' equation, under stochastic initial conditions. These are assumed to be of the shot noise type with the Gibbs-Cox process driving the spatial distribution of the "bumps." In certain cases, this work extends an earlier effort by Surgailis and Woyczynski, where only noninteracting "bumps" driven by the traditional doubly stochastic Poisson process were considered. In contrast to the previous work by Bulinski and Molchanov, a non-Gaussian scaling limit of the statistical solutions is discovered. 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Burgers' equation is known to describe various physical phenomena such as nonlinear and shock waves, distribution of self-gravitating matter in the universe and so forth.</description><subject>35H53</subject><subject>60H15</subject><subject>76F20</subject><subject>Burger equation</subject><subject>Burgers turbulence</subject><subject>Gibbs-Cox random field</subject><subject>Mathematical theorems</subject><subject>Mathematics</subject><subject>multiple Wiener-Ito integral</subject><subject>Non Gaussianity</subject><subject>Particle interactions</subject><subject>Perceptron convergence procedure</subject><subject>Poisson process</subject><subject>scaling limits</subject><subject>Shot noise</subject><subject>Turbulence</subject><subject>White noise</subject><issn>1050-5164</issn><issn>2168-8737</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1995</creationdate><recordtype>article</recordtype><recordid>eNptkDFrwzAQhUVpoWnauUsH_wEnd5JsyWNqmrRgKJRkNrJ0Lg5OFKQY2n_fhIRk6fR4x71v-Bh7RpggRzk13uymiEoBSKXkDRtxzHWqlVC3bISQQZphLu_ZQ4xrAChkoUZssuiaJqal_0m-zNb5TTLvqHcxOZTkdQjfFGKyHEIz9LS19MjuWtNHejrnmK3mb8vyPa0-Fx_lrEotL3CfCi1E0aIyEqyAnNCpJgNhuAXiXEBrNOWO6NByktoBySxzGnWuXUEaxJjNTtxd8Guyexps37l6F7qNCb-1N11drqrz9RxHAfVVwIExPTFs8DEGai9zhPqo7J_Fy2mxjnsfLu-cy0yAFn_YFGgL</recordid><startdate>19950501</startdate><enddate>19950501</enddate><creator>Funaki, T.</creator><creator>Surgailis, D.</creator><creator>Woyczynski, W. 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| source | Jstor Complete Legacy; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Project Euclid Complete; JSTOR Mathematics & Statistics |
| subjects | 35H53 60H15 76F20 Burger equation Burgers turbulence Gibbs-Cox random field Mathematical theorems Mathematics multiple Wiener-Ito integral Non Gaussianity Particle interactions Perceptron convergence procedure Poisson process scaling limits Shot noise Turbulence White noise |
| title | Gibbs-Cox Random Fields and Burgers Turbulence |
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