Compute approximations to Fourier transforms of continuous-time signals with finite discrete time methods. Take advanced courses in signal processing (image, speech, audio, etc.), communications, ...

Physicists have shown that Markov processes, widely used to model complex systems, must unfold over a larger space than previously assumed. Scientists believe that time is continuous, not discrete ...

Moreover, an example is constructed demonstrating that this bound is asymptotically exact for all $\delta > 0$. The result for discrete time martingales is then used to derive the corresponding bound ...

Until relatively recently, however, sound statistical methods for answering such questions have not been readily available. In this article, by empirical example and mathematical argument, we ...