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Let Vx,k(t) denote the component of velocity in the x direction of the kth electron at time t. The total current denoted by I(t) is the sum of all electron currents in the x direction nAL or that the location of the walker is governed approximately by a Gaussian law. 1 8 6 4 2 0 –2 100 200 300 400 500 (c) Figure 2. Plots of realizations from numerical approximations to the Wiener process for various values of s and T. In all cases, Ͱ ϭ 1. 1. where n is the number of electrons per cubic centimeter and q is the charge of an electron.

Furthermore, when the signal is in addition wide-sense stationary, then the joint statistics are shift invariant, and as such, the signal is also strictly stationary. Gaussian noise is further differentiated by the nature of the mean functions and the correlation functions. When the correlation function is given by RX(␶) ϭ N0 /2ͳ(␶), then the signal is said to be Gaussian White Noise, which is the single most common model in noise analysis. In this case, each time sample will be independent from all others and have infinite variance.

THE WHISTLER PHENOMENON A lightning discharge radiates electromagnetic energy over a wide range of frequencies extending beyond those of visible light. Radiation in a relatively low frequency range, 300 Hz to 30 kHz, is the source of whistlers that propagate through the ionosphere and magnetosphere in the whistler mode. This mode of propagation is possible only in a magnetized plasma at frequencies below both the electron plasma frequency and electron gyrofrequency. Propagation is strongly influenced by the geomagnetic field and is characterized by low propagation speeds that vary with frequency.

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