August 2014
Intermediate to advanced
424 pages
11h 25m
English
Content preview from Brownian Motion, 2nd Edition
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19 Stochastic differential equations
The ordinary differential equation 
, x(0) = x0, describes the position xt of a particle which moves with speed b(s, x) depending on time and on the current position. One possibility to take into account random effects, e. g. caused by measurement errors or hidden parameters, is to add a random perturbation which may depend on the current position. This leads to an equation of the form
Letting ∆t → 0 we get the following equation for stochastic differentials, cf. Section 17.1,
Since (19.1) is a formal ...
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