The easiest way in Illustrator is to use a color to transparent gradient fill. Then use
Effect > Pixelate > Pointillize on that gradient fill.
Cell Size of the effect will result in more or less speckle clumps. And altering the span of the gradient can control how much drop off there may be.
This effect will be an embedded raster image with a clipping mask when saved or exported to flat file formats such as EPS. However, the ppi of the effect will automatically adjust according to
Effects > Document Raster Effects Settings within Illustrator if the effect is kept "live".
There are several effects which will achieve similar, but different, results... you'll have to experiment to find the one you're specifically looking for....