Stochastic Process with Memory
Full Title
The notion of long range dependence has, clearly, something to do with memory in a stochastic process.. The “specialness” of long memory indicates that most stationary stochastic processes do not have it. [1]
A stationary process is a stochastic process whose unconditional joint probability distribution does not change when shifted in time.
Clearly a photon that as originated in the early universe has a very long memory.
Context
The first serious argument that this can be important is in a series of papers of B. Mandelbrot and his co-authors, e.g. Mandelbrot[2] and Mandelbrot and Wallis.[3] It is also due to the influence of these early papers and subsequent publications of Mandelbrot (especially Mandelbrot[4]) that long range dependence has also become associated with scaling and fractal behavior.
References
- ↑ GENNADY SAMORODNITSKY LONG RANGE DEPENDENCE Cornell (2007?) https://people.orie.cornell.edu/gennady/techreports/LRD-NOW.pdf
- ↑ B. Mandelbrot (1965): Une classe de processus stochastiques homothetiques a soi; application a loi climatologique de H.E. Hurst. Comptes Rendus Acad. Sci. Paris 240:3274–3277
- ↑ B. Mandelbrot and J. Wallis: Noah, Joseph and operational hydrology. Water Resources Research 4:909–918
- ↑ B. Mandelbrot : The Fractal Geometry of Nature. W.H. Freeman and Co., San Francisco (1983)
