Symmetries of stochastic differential equations

• This chapter deals with applications of the group analysis method to stochastic differential equations. These equations are often obtained by including random fluctuations in differential equations, which have been deduced from phenomenological or physical view. In contrast to deterministic differential equations, only few attempts to apply group analysis to stochastic differential equations can be found in the literature. It is worth to note that this theory is still developing. Before defining an admitted symmetry for stochastic differential equations an introduction into the theory of this type of equations is given. The introduction includes the discussion of a stochastic integration, a stochastic differential and a change of the variables (Itô formula) in stochastic differential equations. Applications of the Itô formula are considered in the next section which deals with the linearization problem. The Itô formula and the change of time in stochastic differential equations are the main tools of defining admitted transformations for them. After introducing an admitted Lie group and supporting material of the introduced definition, some examples of applications of the given definition are studied.

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NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

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