A NEW NOISE DEPENDING ON A SPACE PARAMETER AND ITS TRANSFORMATIONS

We introduce a new noise P′(υ,λ), with a space parameter υ and the intensity λ noting that the characteristic of Poisson type process depends on the intensity. A new noise P′(υ,λ) is different with the time derivative of Poisson process P(t). In this paper, the invariance of the intensity λ under the transformations : dilation and reflection is discussed. In addition, it is interesting to see how the intensity changes when the exponent of a stable process changes to its reciprocal.