Affine processes on positive semidefinite d $\times$ d matrices have jumps of finite variation in dimension d > 1

Details Affine processes on positive semidefinite d $\times$ d matrices have jumps of finite variation in dimension d > 1 Affine processes on positive semidefinite d $\times$ d matrices have jumps of finite variation in dimension d > 1

2011-04-05

arxiv.org/abs/1104.0784v3

Mathematics

Probability

Proof of main result extended, changed title

Scientific paper

The theory of affine processes on the cone of positive semidefinite d x d matrices has been established in a joint work with Cuchiero, Filipovic and Teichmann (2011). We confirm the conjecture stated therein that in dimension d greater than one this process class does not exhibit jumps of infinite total variation. This is a geometric phenomenon and in contrast to the situation on the positive real line (Kawazu and Watanabe, 1974). As an application we prove that the exponentially affine property of the Laplace transform carries over to the Fourier-Laplace transform, in the case that the diffusion coefficient is zero or invertible.

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