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Sampling from transition equation (state space model) 
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#1
Nov1310, 02:42 AM

P: 16

Hi.
Consider the following state space equation [tex]x_k = f(x_{k1},v_k)[/tex] where f(.) is a nonlinear function and v_k is a white Gaussian noise (independent of state). I want to generate samples according to [tex] p(x_k  x_{k1} = x_{k1}^i) [/tex] for a particular [tex]x_{k1}^i[/tex]. I've seen people generate samples [tex] v_k^j [/tex] from [tex] p(v) [/tex] (which is a Gaussian) and consider [tex] x_k^{(i,j)} = f(x_{k1}^i,v_k^j) [/tex] as samples generated according to [tex] p(x_k  x_{k1} = x_{k1}^i) [/tex]. I can understand the intuition behind this approach, but can you suggest any mathematical proof? Thanks, K. 


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