Employing the new regression tests for Convergence, Club Convergence and Clustering proposed by Phillips and Sul (2007), this paper models and analyzes the behavior of China‘s energy sectors. Energy market ̳convergence clusters‘ are identified using new price data and their regional spatial distributions are mapped for four major fuel types; coal, gasoline, diesel and electricity. It is found t...

Ω |∇u| N ) 1 N . The dual space is denoted W−1,N ′ , where N ′ is the Hölder conjugate of N , and has the associated norm ‖ · ‖∗. Denote strong convergence by “→”, weak convergence by “⇀” and convergence in the sense of measure (or distributions) as “⇀∗”. Unless otherwise denoted, integration is performed over the domain Ω. Specific constraints on e(x, u) and h(x) are described later, but we no...

It is shown that the injective tensor product of positive vector measures in certain Banach lattices is jointly continuous with respect to the weak convergence of vector measures. This result is obtained by a diagonal convergence theorem for injective tensor integrals. Our approach to this problem is based on Bartle’s bilinear integration theory. 2000 Mathematics subject classification: primary...

Convergence, consistency, stability and pathwise positivity of balanced Milstein methods for numerical integration of ordinary stochastic differential equations (SDEs) are discussed. This family of numerical methods represents a class of highly efficient linear-implicit schemes which generate mean square converging numerical approximations with qualitative improvements and global rate 1.0 of me...

We deene an Euler type weak approximation for solutions of nonlinear diiusion processes. We nd the rate of convergence of this scheme in weak form. As in the diiusion case the weak rate of convergence is better than the strong one. The proof uses the integration by parts formula of Malliavin calculus.