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One way to model this behavior is called stochastic rationality. It is assumed that each agent has an unobserved state, which can be considered a random variable. Given that state, the agent behaves rationally. In other words: each agent has, not a single preference-relation, but a distribution over preference-relations (or utility functions).
The word stochastic in English was originally used as an adjective with the definition "pertaining to conjecturing", and stemming from a Greek word meaning "to aim at a mark, guess", and the Oxford English Dictionary gives the year 1662 as its earliest occurrence. [1]
The definition of a stochastic process varies, [67] but a stochastic process is traditionally defined as a collection of random variables indexed by some set. [ 68 ] [ 69 ] The terms random process and stochastic process are considered synonyms and are used interchangeably, without the index set being precisely specified.
A simple example may help to explain how the Gillespie algorithm works. Consider a system of molecules of two types, A and B . In this system, A and B reversibly bind together to form AB dimers such that two reactions are possible: either A and B react reversibly to form an AB dimer, or an AB dimer dissociates into A and B .
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.
Indeed, this randomization principle is known to be a simple and effective way to obtain algorithms with almost certain good performance uniformly across many data sets, for many sorts of problems. Stochastic optimization methods of this kind include: simulated annealing by S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi (1983) [10] quantum annealing
Here, the intuition is the same as in the construction of the traditional maximum score estimator: the agent is more likely to choose the choice that has the higher observed part of latent utility. Under certain conditions, the smoothed maximum score estimator is consistent, and more importantly, it has an asymptotic normal distribution.
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.