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The set is called the index set [4] [51] or parameter set [28] [136] of the stochastic process. Often this set is some subset of the real line , such as the natural numbers or an interval, giving the set T {\displaystyle T} the interpretation of time. [ 1 ]
Stochastic social science theory is similar to systems theory in that events are interactions of systems, although with a marked emphasis on unconscious processes. The event creates its own conditions of possibility, rendering it unpredictable if simply for the number of variables involved.
In probability theory, a continuous stochastic process is a type of stochastic process that may be said to be "continuous" as a function of its "time" or index parameter. Continuity is a nice property for (the sample paths of) a process to have, since it implies that they are well-behaved in some sense, and, therefore, much easier to analyze.
In the field of mathematical optimization, stochastic programming is a framework for modeling optimization problems that involve uncertainty.A stochastic program is an optimization problem in which some or all problem parameters are uncertain, but follow known probability distributions.
A stochastic simulation is a simulation of a system that has variables that can change stochastically (randomly) with individual probabilities. [1] Realizations of these random variables are generated and inserted into a model of the system. Outputs of the model are recorded, and then the process is repeated with a new set of random values.
Here the model is linear, the objective function is the expected value of a quadratic form, and the disturbances are purely additive. A basic result for discrete-time centralized systems with only additive uncertainty is the certainty equivalence property : [ 2 ] that the optimal control solution in this case is the same as would be obtained in ...
Stochastic dominance is a partial order between random variables. [1] [2] It is a form of stochastic ordering.The concept arises in decision theory and decision analysis in situations where one gamble (a probability distribution over possible outcomes, also known as prospects) can be ranked as superior to another gamble for a broad class of decision-makers.
A stochastic model would be to set up a projection model which looks at a single policy, an entire portfolio or an entire company. But rather than setting investment returns according to their most likely estimate, for example, the model uses random variations to look at what investment conditions might be like.