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1 Introduction to Stochastic Processes

MA636: Introduction to Stochastic processes1 11 Introduction to Stochastic IntroductionStochastic modelling is an interesting and challenging area of proba-bility and statistics. Our aims in this introductory section of the notesare to explain what astochastic processis and what is meant by theMarkov property, give examples and discuss some of the objectivesthat we might have in studying Stochastic DefinitionsWe begin with a formal definition, Astochastic processis a familyof random variables{X }, indexed by a parameter , where belongsto some index set.

1.3 Stochastic and deterministic models Stochastic models can be contrasted with deterministic models. A deterministic model is specified by a set of equations that describe exactly how the system will evolve over time. In a stochastic model, the evolution is at least partially random and if the process is run

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