Organodynamics	Grant Holland, Apr 25, 2014
Slide: Characterizing degrees of uncertainty	Nav Refs Top Bottom Previous Next 90m 90m 45m 45m 25m 25m
A probability space is a representation of chance variation, also called random fluctuation. A probability space can be represented by a symbol, such as “X”, called “random variable”. Also called a “chance variable”. The values that this symbol can take on are the sample points of the sample space. Often, each sample point will also be associated with a numerical value. This is accomplished via a value function v(X). When such a value function exists, the numbers are often substituted for sample point in the random variable. In such a case, the random variable is real valued.	Manifestations of Uncertainty In general, this chance variation, or random fluctuation, represents uncertainty in the behavior of a probability space. However, uncertainty is a general term that represents many specific manifestations –both “good” and “bad” in the real world. These manifestations define various applications domains… Some of these are: - instability - unpredictability - freedom - opportunity - chaos - adaptability
So, chance variation and uncertainty turn out to be very general characterizations of complex dynamical systems whose dynamics are influenced by uncertainty and random fluctuations. A great deal of the interesting aspects of their behavior is characterized by the degree to which they exhibit chance variation and uncertainty.	Therefore, we need mathematical mechanisms to provide these characterizations to probability spaces and to stochastic processes. We shall next look at two such approaches – and select one of them for organodynamics….

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