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Airy Process
The Airy processes are a family of Stationary process, stationary stochastic processes that appear as limit processes in the theory of random growth models and random matrix theory. They are conjectured to be Universality class, universal limits describing the long time, large scale spatial fluctuations of the models in the Kardar–Parisi–Zhang equation#KPZ universality class, (1+1)-dimensional KPZ universality class (Kardar–Parisi–Zhang equation) for many initial conditions (see also KPZ fixed point). The original process Airy2 was introduced in 2002 by the mathematicians Michael Prähofer and Herbert Spohn. They proved that the height function of a model from the (1+1)-dimensional KPZ universality class - the PNG droplet - converges under suitable scaling and initial condition to the Airy2 process and that it is a stationary process with almost surely continuous sample paths. The Airy process is named after the Airy function. The process can be defined through its finite-di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stationary Process
In mathematics and statistics, a stationary process (also called a strict/strictly stationary process or strong/strongly stationary process) is a stochastic process whose statistical properties, such as mean and variance, do not change over time. More formally, the joint probability distribution of the process remains the same when shifted in time. This implies that the process is statistically consistent across different time periods. Because many statistical procedures in time series analysis assume stationarity, non-stationary data are frequently transformed to achieve stationarity before analysis. A common cause of non-stationarity is a trend in the mean, which can be due to either a unit root or a deterministic trend. In the case of a unit root, stochastic shocks have permanent effects, and the process is not mean-reverting. With a deterministic trend, the process is called trend-stationary, and shocks have only transitory effects, with the variable tending towards a determin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
