Simulation and Inference for Stochastic Differential Equations: With R Examples

By T. McMillen. 2008

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where W (t) is the Wiener process. Here b(t,X) is the drift and σ2(t,X) is the variance of the process. Such equations have been successfully used to model an enormous variety of problems in fields as diverse as biology, physics, neuroscience and finance. Most of the examples treated in this volume are drawn from finance. Although only one-dimensional processes are considered, as the author notes, most of the simulation techniques that can be used with one-dimensional processes apply equally well to their multi-dimensional counterparts, and references are provided for multi-dimensional SDE simulations.

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From State Dependent Diffusion to Constant Diffusion in Stochastic Differential Equations by the Lamperti Transform (2010, methodology): “The implication will be discussed further for multivariate processes in Section 4. The term “weak solution” refer to equality in distribution, and strong solutio ns refer to path-wise equality (see Øksendal (2003) for further discuss ion on weak”