10 3 Let fXt t $ 0g be a continuous time continuous state Markov process whose transition PDF fx t x0 t0 satisfies the following forward Kolmogorov equation f t 5 2 x at xf 1 1 2 2 x2 bt xf Assume that at x 5 at and bt x 5 bt Show that the forward Kolmogorov equation can be reduced to f t 5 1 2 2 f...

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10.3 Let fXt; t $ 0g be a continuous-time continuous-state Markov process whose transition PDF fx; t;...

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10.3 Let fXðtÞ; t $ 0g be a continuous-time continuous-state Markov process whose transition PDF fðx; t; x0; t0Þ satisfies the following forward Kolmogorov equation: @f @t 5 2 @ @x ðaðt; xÞfÞ 1 1 2 @2 @x2 ðbðt; xÞfÞ Assume that aðt; xÞ 5 aðtÞ and bðt; xÞ 5 bðtÞ. Show that the forward Kolmogorov equation can be reduced to @f @t 5 1 2 @2 f @x2 Also, show that the corresponding distribution is Gaussian.

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