A family of geometrical entropies for stochastic processes in path space

✍ Scribed by Guy Jumarie

• Publisher: Elsevier Science
• Year: 1992
• Tongue: English
• Weight: 904 KB
• Volume: 184
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/0378-4371(92)90320-p

✦ Synopsis

One can obtain a meaningful concept of informational entropy of deterministic functions as a direct consequence of Shannon information theory. When one applies this model to the trajectory generated by a stochastic process (for instance a process driven by a Langevin equation), one arrives at new concepts of random entropy and of graph entropy (different from path entropy via path integral) for measuring the amount of uncertainty involved in this random phenomenon. The consistency with Shannon theory is complete. Mainly these definitions are not a new modelling made for convenience, but rather are straightforward consequences of classical results; they are geometrical entropies directly related to the theory of fractals and complexity.