Let Xt be a linear process defined by Xt=Σ k=0 ∞ψ kε t-k, where {ψ k,k≥ 0} is a sequence of real numbers and {ε k, k = 0,±1,±2,...} is a sequence of random variables. Two basic results, on the ...

In recent papers, McLeish and others have obtained invariance principles for weak convergence of martingales to Brownian motion. We generalize these results to prove that solutions of discrete-time ...

Symmetry and invariance lie at the heart of modern physical theories, serving as guiding principles in our understanding of the natural world. These ideas are central to elucidating conservation laws ...

The more crucial a physical law is, the more important it is to keep testing it. One of the most important laws formulated in the last century or so is Albert Einsteinэs principle of invariance, which ...