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.

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,...

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...