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SummaryThis report presents an approach to stochastic programming. It treats mainly the difficulties arising in formulating the problem and the possibilities to derive a deterministic problem by which it can be replaced. In a sense the approach of this report unifies different viewpoints on stochastic programming problems as they have been published in the literature.

1 What is a Stochastic Process? -- 2 Results from Probability Theory -- 2.1 Introduction to probability theory -- 2.2 Bivariate distributions -- 2.3 Multivariate distributions -- 2.4 Probability generating functions -- 2.5 Characteristic functions -- 3 The Random Walk -- 3.1 The unrestricted random walk -- 3.2 Types of stochastic process -- 3.3 The gambler's ruin -- 3.4 Generalisations of the random-walk model -- 4 Markov Chains -- 4.1 Definitions -- 4.2 Equilibrium distributions -- 4.3 Applications -- 4.4 Classification of the states of a Markov chain -- 5 The Poisson Process -- 6 Markov Chalns with Continuous Time Parameters -- 6.1 The theory -- 6.2 Applications -- 7 Non-Markov Processes in Continuous Time with Discrete State Spaces -- 7.1 Renewal theory -- 7.2 Population processes -- 7.3 Queuing theory -- 8 Diffusion Processes -- Recommendations For Further Reading.

We study stochastic choice as the outcome of deliberate randomization. We derive a general representation of a stochastic choice function where stochasticity allows the agent to achieve from any set the maximal element according to her underlying preferences over lotteries. We show that in this model stochasticity in choice captures complementarity between elements in the set, and thus necessarily implies violations of Regularity/Monotonicity, one of the most common properties of stochastic choice. This feature separates our approach from other models, e.g., Random Utility. (JEL D80, D81)