most recent 30 from http://mathoverflow.net 2013-05-25T07:43:58Z http://mathoverflow.net/feeds/question/80230 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/80230/relative-entropy-for-diffusion-processes unknown (google) 2011-11-06T18:33:53Z 2012-08-17T04:43:13Z

<p>It is possible to define the relative entropy between to diffusion processes using Girsanov theorem <strong>only in the case where the diffusion coefficients are the same</strong>. Could you explain why it is not posssible to define a relative entropy between the laws of the two following processes: $$dx_1(t)=f(x_1(t))dt +\sigma_1 dW_t$$ and $$dx_2(t)=f(x_2(t))dt +\sigma_2 dW_t$$ when $\sigma_1 \neq \sigma_2$ ?</p> <p>Beyond the problem of absolute continuity, is not there a way to compare both laws ?</p>

http://mathoverflow.net/questions/80230/relative-entropy-for-diffusion-processes/104891#104891 brownck 2012-08-17T04:43:13Z 2012-08-17T04:43:13Z

<p>This is not an answer to your question, but can you explain and perhaps give a reference to your statement:</p> <p>It is possible to define the relative entropy between to diffusion processes using Girsanov theorem only in the case where the diffusion coefficients are the same. </p>