Showing 1 - 10 of 11
Persistent link: https://www.econbiz.de/10009215413
Non-Gaussian limiting distributions of the rescaling solutions of the heat equation for non-Gaussian initial data with long-range dependence are discribed in terms of their multiple stochastic integral representations.
Persistent link: https://www.econbiz.de/10008875329
Gaussian and non-Gaussian limiting distributions of the rescaled solutions of the fractional (in time) diffusion-wave equation for Gaussian and non-Gaussian initial data with long-range dependence are described in terms of multiple Wiener-Itô integrals.
Persistent link: https://www.econbiz.de/10005074566
A class of stochastic fractional-order differential models with homogeneous boundary conditions on a fractal set is introduced. The corresponding solution class satisfies a weak-sense Markov condition with respect to domains with fractal boundary. Some examples are given which provide a...
Persistent link: https://www.econbiz.de/10005259255
An existence and uniqueness theorem is proved for a quasilinear stochastic evolution equation with an additive noise in the form of a stochastic integral with respect to a Hilbert space-valued fractional Borwnian motion. Ideas of the finite-dimensional approximation by the Galerkin method are used.
Persistent link: https://www.econbiz.de/10005138136
Persistent link: https://www.econbiz.de/10005285243
The least-squares linear inverse estimation problem for random fields is studied in a fractional generalized framework. First, the second-order regularity properties of the random fields involved in this problem are analysed in terms of the fractional Sobolev norms. Second, the incorporation of...
Persistent link: https://www.econbiz.de/10005199792
A fractional version of the heat equation, involving fractional powers of the negative Laplacian operator, with random initial conditions of exponential type, is introduced. Two cases are considered, depending on whether the Hopf-Cole transformation of such random initial conditions coincides,...
Persistent link: https://www.econbiz.de/10008873794
This paper is concerned with the linear regression model in which the variance of the dependent variable is proportional to an unknown power of its expectation. A nonlinear least squares estimator for the model is derived and shown to be strongly consistent and asymptotically normally...
Persistent link: https://www.econbiz.de/10008873940
Persistent link: https://www.econbiz.de/10010908315