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Asymptotic normality of the solutions of the initial-value problems for multidimensional Burgers' equation with weakly dependent possible non-Gaussian initial condition is proved. 相似文献
4.
Beghin Luisa Knopova Viktoria P. Leonenko Nikolai N. Orsingher Enzo 《Journal of statistical physics》2000,99(3-4):769-781
We analyze the asymptotic behavior of the rescaled solution to the linear Korteweg–de Vries equation when the initial conditions are supposed to be random and weakly dependent. By means of the method of moments we prove the Gaussianity of the limiting process and we present its correlation function. The same technique is applied to the analysis of another third-order heat-type equation. 相似文献
5.
Spherical measures of exceeding a low level are considered for strongly dependent chi-square fields. The limit distributions are sums of multiple stochastic integrals.Kiev University. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 68, pp. 118–128, 1989. 相似文献
6.
We prove a central limit theorem for integral functionals of nonlinear transforms of homogeneous, isotropic Gaussian random vector fields.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 8, pp. 1057–1063, August, 1990. 相似文献
7.
We study the thermal force bending of an elastoplastic three-layer beam with a rigid filler; the beam is connected with an
elastic foundation. The broken normal hypothesis is adopted to describe the kinematics of a packet nonsymmetric with respect
to the thickness. The foundation reaction is described by Winkler’s model. The system of equilibrium equations and its exact
solution in displacements are obtained and numerical results for a three-layer metal-polymeric beam are presented. 相似文献
8.
Limiting distributions of the parabolically rescaled solutions of the heat equation with singular non-Gaussian initial data with long-range dependence are described in terms of their multiple stochastic integral representations. 相似文献
9.
The reordering of the multidimensional exponential quadratic operator in coordinate-momentum space (see X. Wang, C.H. Oh and L.C. Kwek (1998). J. Phys. A.: Math. Gen.
31:4329–4336) is applied to derive an explicit formulation of the solution to the multidimensional heat equation with quadratic external potential and random initial conditions. The solution to the multidimensional Burgers equation with quadratic external potential under Gaussian strongly dependent scenarios is also obtained via the Hopf-Cole transformation. The limiting distributions of scaling solutions to the multidimensional heat and Burgers equations with quadratic external potential are then obtained under such scenarios.
AMS Subject Classifications: 60G60, 60G15, 62M15, 60H15 相似文献
10.
O.?E.?Barndorff-NielsenEmail author N.?N.?Leonenko 《Methodology and Computing in Applied Probability》2005,7(3):335-352
Stationary processes with prescribed one-dimensional marginal laws and long-range dependence are constructed. The asymptotic
properties of the spectral densities are studied. The possibility of Mittag-Leffler decay in the autocorrelation function
of superpositions of Ornstein-Uhlenbeck type processes is proved.
AMS 2000 Subject Classification Primary 60E07, 60G10, 60G18
Secondary 62M10, 62P05
Supported by the Danish National Research Foundation and EPSRC grant RCMT091.
Partially supported by the ARC grants DP 0345577, DP0559807 and EPSRC grant RCMT091. 相似文献