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 Jul 21 comment Is there a map that maps the mean vector and the variance matrix of a multivariate lognormal to its location vector and diffusion matrix? Good that you found a potential solution. Jul 21 comment Is there a map that maps the mean vector and the variance matrix of a multivariate lognormal to its location vector and diffusion matrix? Also, check this post just in case it is useful to you. Jul 21 comment Is there a map that maps the mean vector and the variance matrix of a multivariate lognormal to its location vector and diffusion matrix? I would suggest you could do this to make sure the resultant transformation is correct: Sample some data from the known mean and std dev of the obtained lognormal transformation. Take log of those data and check if their distribution is normal or not. if your transformed lognormal distribution is correct then the log of those data should give you a normal distribution. Jul 21 comment Is there a map that maps the mean vector and the variance matrix of a multivariate lognormal to its location vector and diffusion matrix? Nicola: To clarify my few "side comments" that I gave earlier, I would like to make two points. 1) not all covariance matrix you obtain numerically will have the property of "covariance" or "correlation" matrix, which is that the covariance matrix is supposed to be positive semi-definite and not all estimates are guaranteed to have that property. 2) I checked if the transformation is PD provided it was PD before, however, I could not find any simple explanation for that. Jul 20 comment Is there a map that maps the mean vector and the variance matrix of a multivariate lognormal to its location vector and diffusion matrix? If the covariance is standard then it'll have sill, hence, it'll be positive definite. However, if you're numerical covariance does not have a sill then it's not positive definite. It's the same thing I believe as stationarity Jul 20 comment Is there a map that maps the mean vector and the variance matrix of a multivariate lognormal to its location vector and diffusion matrix? I believe since you're transforming from one standard distribution to another standard distribution so that should be fine. Maybe either you're 1) missing log while transforming. Sometimes the distribution you have is normal so make sure you're taking care of transforming it to log normal first by taking log. 2) it could also be an error in coding somewhere. Jul 20 comment Is there a map that maps the mean vector and the variance matrix of a multivariate lognormal to its location vector and diffusion matrix? Where did you get that transformation from? Does the field exhibit stationarity or in other words the variances of blocks of data should be constant. It'll be positive definite if it's stationary. Jul 20 comment Issues with finite-difference implicit solution of Advection-Diffusion-Reaction eqn @uranix: I sent you the results obtained after implementing your discretization scheme, but those results are still not coming as expected. Were you able to look at it? Thank you so much. Jul 20 comment Bounded Matrix-Vector Multiplication Zircht: I don't think the condition you proposed on boundedness includes all possibilities. $\| Ax \|$ will, in fact, be always bounded for given conditions. You may want to check the explanation below in the answer. Jul 20 answered Physical applications of Chebyshev's equation. Jul 20 comment Solution of Second order ODE: theoretical question Okay. You may want to edit your question then to clarify that those solutions which do not have exponentials in them. Jul 20 answered Solution of Second order ODE: theoretical question Jul 20 answered Bounded Matrix-Vector Multiplication Jul 20 comment Is there a map that maps the mean vector and the variance matrix of a multivariate lognormal to its location vector and diffusion matrix? You could probably get more help if you edit your question in a more structured format ( e.g. a) Your problem setting, b) What issues you have, and c) If you have tried something) than writing long paragraphs. Jul 19 comment Issues with finite-difference implicit solution of Advection-Diffusion-Reaction eqn Yes, they're always greater than zero or zero in which case there will be no advection. Jul 19 comment Issues with finite-difference implicit solution of Advection-Diffusion-Reaction eqn Here's the link to my discretization scheme. Jul 19 comment Issues with finite-difference implicit solution of Advection-Diffusion-Reaction eqn uranix: then what should it be? Jul 19 comment Issues with finite-difference implicit solution of Advection-Diffusion-Reaction eqn I am taking $\nabla \cdot (D \nabla C)$ term as $\nabla D \cdot \nabla C + D \nabla ^{2} C$ Jul 19 comment Issues with finite-difference implicit solution of Advection-Diffusion-Reaction eqn But I am not getting that error. You can remove the edge_order=2 term, it will take 1 by default then. Jul 19 revised Issues with finite-difference implicit solution of Advection-Diffusion-Reaction eqn added 16 characters in body