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gradient wrt transition probabilities

Using the chain rule,


By differentiating eqn.1.21 wrt tex2html_wrap_inline2892 we get,


and differentiating (a time shifted version of) eqn 1.2 wrt tex2html_wrap_inline2894


Eqns. 1.23,1.24 and 1.25 give, tex2html_wrap_inline2898 , and substituting this quantity in eqn.1.22 (keeping in mind that tex2html_wrap_inline2900 in this case), we get the required result,


Narada Warakagoda
Fri May 10 20:35:10 MET DST 1996

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