Suppose $\frac{dx}{dt}=ax+b$ and then assume that $a=c+g$ where $g$ is a Wiener process.
How can I obtain from a differential equation a stochastic version?
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stochastic-processes
sde
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1What's the question? – 2010-12-01
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0This could be interesting, so please extend your question (a little more flesh is needed!) – 2010-12-01
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0Ok, I will try, Suppose a deterministic dynamical system defined using the ordinary differential equation dx/dt=ax+b Then what happens if the system is shaken by a white noise process, for instance if the parameter a stops being a constant and assumes a form as a=c+g where g is a parameter and c is a white noise process. Then the sde should be written in a form dx=((c+g)x+b)dt+σ(_)dz What is the algebra from ode to sde? And what if the functional form of σ(_) ? Any reference or suggestions? thanks!! – 2010-12-01