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In information theory and statistics, negentropy is used as a measure of distance to normality. [4] [5] [6] Out of all distributions with a given mean and variance, the normal or Gaussian distribution is the one with the highest entropy.
Biological processes are regulated by many means; examples include the control of gene expression, protein modification or interaction with a protein or substrate molecule. Homeostasis: regulation of the internal environment to maintain a constant state; for example, sweating to reduce temperature
In stochastic analysis a random process is a predictable process if it is possible to know the next state from the present time. The branch of mathematics known as Chaos Theory focuses on the behavior of systems that are highly sensitive to initial conditions. It suggests that a small change in an initial condition can completely alter the ...
In stochastic analysis, a part of the mathematical theory of probability, a predictable process is a stochastic process whose value is knowable at a prior time. The predictable processes form the smallest class that is closed under taking limits of sequences and contains all adapted left-continuous processes. [clarification needed]
The concept of allostasis, maintaining stability through change, is a fundamental process through which organisms actively adjust to both predictable and unpredictable events... Allostatic load refers to the cumulative cost to the body of allostasis, with allostatic overload... being a state in which serious pathophysiology can occur...
Hindsight bias is more likely to occur when the outcome of an event is negative rather than positive. [14] This is a phenomenon consistent with the general tendency for people to pay more attention to negative outcomes of events than positive outcomes.
Then there exist a martingale M = (M n) n∈I and an integrable predictable process A = (A n) n∈I starting with A 0 = 0 such that X n = M n + A n for every n ∈ I. Here predictable means that A n is -measurable for every n ∈ I \ {0}. This decomposition is almost surely unique. [2] [3] [4]
Consider a stochastic process X : [0, T] × Ω → R, and equip the real line R with its usual Borel sigma algebra generated by the open sets.. If we take the natural filtration F • X, where F t X is the σ-algebra generated by the pre-images X s −1 (B) for Borel subsets B of R and times 0 ≤ s ≤ t, then X is automatically F • X-adapted.