FRACTIONAL PROCESS Meaning and
Definition
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A fractional process is a mathematical concept used in probability theory and stochastic processes to describe the behavior of random variables over a continuous or discrete time period. It refers to a stochastic process whose increments or changes occur in a fractional manner or exhibit fractal-like properties.
In a fractional process, the increments or changes of the process are not constrained to integer values, but can take on fractional values. This property allows for more flexibility and accuracy in modeling and analyzing complex systems that exhibit non-linear or irregular behaviors. Fractional processes are particularly useful in capturing long-term dependencies and memory effects that cannot be effectively captured by traditional processes.
The most well-known example of a fractional process is the fractional Brownian motion, developed by the French mathematician Benoît Mandelbrot. It is a continuous-time stochastic process that exhibits self-similarity and long-range dependence. The increments of fractional Brownian motion are not independent, but instead exhibit a correlation structure that decreases with increasing time lag. This property allows it to model phenomena with long-term memory, such as stock prices, turbulence in fluid dynamics, and network traffic patterns.
In summary, a fractional process is a stochastic process that allows for modeling of complex systems with fractional increments and fractal-like properties. It is a powerful tool in probability theory and stochastic processes for capturing long-term dependencies and non-linear behaviors in various fields of science and engineering.
Common Misspellings for FRACTIONAL PROCESS
- dractional process
- cractional process
- vractional process
- gractional process
- tractional process
- rractional process
- feactional process
- fdactional process
- ffactional process
- ftactional process
- f5actional process
- f4actional process
- frzctional process
- frsctional process
- frwctional process
- frqctional process
- fraxtional process
- fravtional process
- fraftional process
Etymology of FRACTIONAL PROCESS
The term "fractional process" does not have a specific etymology as it is a combination of two separate words: "fractional" and "process". However, we can examine the origin of each word individually.
1. Fractional: The word "fractional" comes from the Latin word "fractus", which means "broken" or "divided". The term evolved from the Latin phrase "fractus pars" meaning "broken part". Over time, "fractus" transformed into "fractusio" in Late Latin, and eventually into "fraction" in English.
2. Process: The word "process" originates from the Latin verb "procedere", which means "to go forward" or "to proceed". In Latin, it referred to an onward movement or progress. The term gradually morphed into "processus", a noun meaning "progression" or "advance".
Similar spelling word for FRACTIONAL PROCESS
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