Solving Matrix RODEs with 1/f noise

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I've been trying to solve differential equations of the form



$$dotrho=omega Lrho$$



where $omega=omega(t)$ is scalar 1/f (or pink) noise and $L$ and $rho$ are matrices.



I wanted to know if there were any recommended numerical schemes to solve it. I have looked into the Taylor-RODE scheme (described here: https://pdfs.semanticscholar.org/f357/b5b871bc704659bf18507135eea9f57a5fa4.pdf) but it doesn't seem very efficient (involves various integrals and such). I was hoping to find a nice efficient SDE-resembling scheme to solve it. I saw some papers on forming nonlinear and/or coupled SDEs for just 1/f noise.



https://arxiv.org/pdf/1603.03013.pdf



http://web.vu.lt/tfai/j.ruseckas/files/presentations/Turkey-2012.pdf



https://arxiv.org/pdf/1003.1155.pdf



I wanted to know if anyone had implemented solutions to SDEs like these and if anyone has a good idea on how to extend it properly and efficently to these matrix equations.



If there are any other nice schemes or ideas you have, please let me know as well!



Thanks!




stochastic-processes stochastic-calculus random-matrices sde




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    up vote
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    down vote

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    I've been trying to solve differential equations of the form



    $$dotrho=omega Lrho$$



    where $omega=omega(t)$ is scalar 1/f (or pink) noise and $L$ and $rho$ are matrices.



    I wanted to know if there were any recommended numerical schemes to solve it. I have looked into the Taylor-RODE scheme (described here: https://pdfs.semanticscholar.org/f357/b5b871bc704659bf18507135eea9f57a5fa4.pdf) but it doesn't seem very efficient (involves various integrals and such). I was hoping to find a nice efficient SDE-resembling scheme to solve it. I saw some papers on forming nonlinear and/or coupled SDEs for just 1/f noise.



    https://arxiv.org/pdf/1603.03013.pdf



    http://web.vu.lt/tfai/j.ruseckas/files/presentations/Turkey-2012.pdf



    https://arxiv.org/pdf/1003.1155.pdf



    I wanted to know if anyone had implemented solutions to SDEs like these and if anyone has a good idea on how to extend it properly and efficently to these matrix equations.



    If there are any other nice schemes or ideas you have, please let me know as well!



    Thanks!




    stochastic-processes stochastic-calculus random-matrices sde




    share|cite|improve this question





















      up vote
      1
      down vote

      favorite









      up vote
      1
      down vote

      favorite











      I've been trying to solve differential equations of the form



      $$dotrho=omega Lrho$$



      where $omega=omega(t)$ is scalar 1/f (or pink) noise and $L$ and $rho$ are matrices.



      I wanted to know if there were any recommended numerical schemes to solve it. I have looked into the Taylor-RODE scheme (described here: https://pdfs.semanticscholar.org/f357/b5b871bc704659bf18507135eea9f57a5fa4.pdf) but it doesn't seem very efficient (involves various integrals and such). I was hoping to find a nice efficient SDE-resembling scheme to solve it. I saw some papers on forming nonlinear and/or coupled SDEs for just 1/f noise.



      https://arxiv.org/pdf/1603.03013.pdf



      http://web.vu.lt/tfai/j.ruseckas/files/presentations/Turkey-2012.pdf



      https://arxiv.org/pdf/1003.1155.pdf



      I wanted to know if anyone had implemented solutions to SDEs like these and if anyone has a good idea on how to extend it properly and efficently to these matrix equations.



      If there are any other nice schemes or ideas you have, please let me know as well!



      Thanks!




      stochastic-processes stochastic-calculus random-matrices sde




      share|cite|improve this question











      I've been trying to solve differential equations of the form



      $$dotrho=omega Lrho$$



      where $omega=omega(t)$ is scalar 1/f (or pink) noise and $L$ and $rho$ are matrices.



      I wanted to know if there were any recommended numerical schemes to solve it. I have looked into the Taylor-RODE scheme (described here: https://pdfs.semanticscholar.org/f357/b5b871bc704659bf18507135eea9f57a5fa4.pdf) but it doesn't seem very efficient (involves various integrals and such). I was hoping to find a nice efficient SDE-resembling scheme to solve it. I saw some papers on forming nonlinear and/or coupled SDEs for just 1/f noise.



      https://arxiv.org/pdf/1603.03013.pdf



      http://web.vu.lt/tfai/j.ruseckas/files/presentations/Turkey-2012.pdf



      https://arxiv.org/pdf/1003.1155.pdf



      I wanted to know if anyone had implemented solutions to SDEs like these and if anyone has a good idea on how to extend it properly and efficently to these matrix equations.



      If there are any other nice schemes or ideas you have, please let me know as well!



      Thanks!





      stochastic-processes stochastic-calculus random-matrices sde





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      asked Jul 25 at 16:46









      Aakash Lakshmanan

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