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Jun
30
comment Cholesky decomposition and variance
It actually may be better to write it as just $Cov(A+BZ)=B^TCov(Z)B$, since of course adding a constant has no effect on variance and so $Cov(A)=0$, a reference can be found here: en.wikipedia.org/wiki/….
Jun
30
comment Cholesky decomposition and variance
$Cov(A + BZ) = Cov(A) + B^TCov(Z)B$. This is a direct result of the linearity of expectation. However it should be clear right away that it definitely can't be just $B$, since the covariance matrix must be positive semi-definite.
Jun
30
answered How do you determine the end behavior of a rational function?
Jun
30
comment When trying to learn analysis from bottom up, what numbers should I first construct?
mathematicians aren't interested in foundations
Jun
24
revised Matrix Dimension's effect on Positive Definiteness
added 39 characters in body
Jun
24
answered Matrix Dimension's effect on Positive Definiteness
Jun
23
comment Default positive/(non-negative) probability distribution
It appears to be a generalization of the exponential distribution for the specification of higher moments. There is no 'equivalent' distribution in the absolute sense, it appears to be equivalent in the sense of maximizing entropy. Whether or not maximizing entropy is the right call for capturing your lack of prior knowledge in the model is entirely up to your own judgement of the problem.
Jun
23
comment Default positive/(non-negative) probability distribution
Note that assuming a normal distribution also requires estimates for the mean and variance. I'm sure there is info online on the average volume of oxygen inhaled per minute/hour whatever.
Jun
23
comment Default positive/(non-negative) probability distribution
If you have some data to calculate the sample mean and sample variance, then you might take a look at this answer: stats.stackexchange.com/questions/83069/…. For a given mean and variance, the normal distribution maximizes entropy, this answer appears to provide the equivalent for a distribution with strictly nonnegative support.
Jun
23
comment What math preparation is needed before reading the mathematical method in financial markets?
measure theoretic probability, stochastic calculus, stochastic differential equations, looking at the table of contents that book is no joke. Even if you knew all that stuff I wouldn't recommend that book for a first pass.
Jun
22
comment Does there exist a function $F(x)$, so that $F'(x) $ is not Riemann integrable?
man wtf, are these objects just anomalies of the real line, why would the universe allow such abominations to exist?
Jun
22
revised How much information does learning this interval give you?
added 105 characters in body
Jun
22
answered How much information does learning this interval give you?
Jun
20
revised What are some Applications of Hermitian Positive Definite matrices?
added 1 character in body
Jun
20
revised What are some Applications of Hermitian Positive Definite matrices?
edited body
Jun
20
revised What are some Applications of Hermitian Positive Definite matrices?
added 2 characters in body
Jun
20
answered What are some Applications of Hermitian Positive Definite matrices?
Jun
17
accepted What property of a matrix causes $\|e^{tA}\|_2$ to oscillate as $t\rightarrow\infty$?
Jun
16
comment Solving a matrix equation using numerical optimization
You can without loss of generality assume that $A$ is symmetric. if $A$ is not positive semi-definite then the function is not bounded below and so the minimum is $-\infty$.
Jun
14
comment Density function of a transformation
$P(Y < a) = P(X^3 < a ) = P(X < \sqrt[3]{a})$