Titlebook: Handbook of Dynamics and Probability; Peter Müller Book 2022 The Editor(s) (if applicable) and The Author(s), under exclusive license to S

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,Ein Gedächtnis kommt niemals allein,is executed. Truncation errors occur when the derivative of a function is replaced by a finite difference approximation. Truncation errors are under the control of the modeler. They can be reduced by decreasing the time step or grid spacing.

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nings of the models that they use. Despite the peculiarities of any applied science, dynamics and probability are the common and indispensable tools in any modeling effort. The book is self-contained, with many978-3-030-88488-8978-3-030-88486-4

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Book 2022 applied sciences who aspire to better understand the conceptual and mathematical underpinnings of the models that they use. Despite the peculiarities of any applied science, dynamics and probability are the common and indispensable tools in any modeling effort. The book is self-contained, with many

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Numerical Algorithmsis executed. Truncation errors occur when the derivative of a function is replaced by a finite difference approximation. Truncation errors are under the control of the modeler. They can be reduced by decreasing the time step or grid spacing.

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Discrete-Time Stochastic ProcessesHere we start to extend the concept of random variables to families of random variables . where the index set is either . (.) or . (.). The first case represents ., the second case represents .. We thus progress up through the general classification of families of random variables.

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Continuous-Time Stochastic ProcessesIn this chapter we consider families of random variables . where time . is continuous, either . or .. We call these families continuous stochastic processes.