Wiener’s test for space-time random walks and its applications

Random walks in space time mixing environments

We prove that random walks in random environments, that are exponentially mixing in space and time, are almost surely diffusive, in the sense that their scaling limit is given by the Wiener measure. 1 The results Random walks in random environments are walks where the transition probabilities are themselves random variables (see [22, 23] for recent reviews of the literature). The environments c...

Space-time velocity correlation function for random walks.

Space-time correlation functions constitute a useful instrument from the research toolkit of continuous-media and many-body physics. Here we adopt this concept for single-particle random walks and demonstrate that the corresponding space-time velocity autocorrelation functions reveal correlations which extend in time much longer than estimated with the commonly employed temporal correlation fun...

Time of random walks

An almost sure invariance principle for random walks in a space-time random environment

We consider a discrete time random walk in a space-time i.i.d. random environment. We use a martingale approach to show that the walk is diffusive in almost every fixed environment. We improve on existing results by proving an invariance principle and considering environments with an L2 averaged drift. We also state an a.s. invariance principle for random walks in general random environments wh...

Application of Single-Frequency Time-Space Filtering Technique for Seismic Ground Roll and Random Noise Attenuation

Time-frequency filtering is an acceptable technique for attenuating noise in 2-D (time-space) and 3-D (time-space-space) reflection seismic data. The common approach for this purpose is transforming each seismic signal from 1-D time domain to a 2-D time-frequency domain and then denoising the signal by a designed filter and finally transforming back the filtered signal to original time domain. ...