# For an affine process, how do we know the second order term is positive definite?

A regular affine process is defined to have the generator

$Af(x) = \sum_{k,l=1}^d(a_{kl}+\langle a_{I,kl},y\rangle)\frac{\partial^2f(x)}{\partial x_k\partial x_l}+\langle b+\beta x,\nabla f(x)\rangle - ...$

see the bottom of page 8 of this following file:

http://web.stanford.edu/~duffie/affine.pdf

My question is, how do we know the matrix $M$, defined by $M_{kl} = (a_{kl}+\langle a_{I,kl},y\rangle)$ is always positive semidefinite? (I assume this must the be the case, but how does one show this? is there a general theorem which tells you this must be the case for the generator of a stochastic process?)

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