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How can I derive analytically or compute numerically the solution to following differential equation

$$ dy/dt = y\cdot X\cdot (y\cdot X - g(y,X))\cdot X $$

where X is a random variable (e.g. from a normal distribution) and g is a known function of y and X, e.g. $g=E[(y\cdot X)^2]$ ?

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  • $\begingroup$ Have a look at ItoProcess and similar. Maybe you could post a more specific example. $\endgroup$ – b.gates.you.know.what Jan 9 '14 at 15:35
  • $\begingroup$ Well, this is a specific example arising e.g. from learning in neural networks. X is a random input to a node and y is the input weight to this node, which changes according to the above equation. I had a look at ItoProcesses, but I am not sure whether I have somehow to convert the above equation to an Ito process or if a different approach is needed. $\endgroup$ – user120162 Jan 9 '14 at 15:45
  • $\begingroup$ Might be able to use WhenEvent, possibly in conjunction with DiscreteVariables (which might change values according to your random distribution). $\endgroup$ – Daniel Lichtblau Jan 9 '14 at 16:16

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