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

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Abstract

The theory of affine processes on the space of positive semidefinite d×d matrices has been established in a joint work with Cuchiero et al. (2011) [4]. We confirm the conjecture stated therein that in dimension d>1 this process class does not exhibit jumps of infinite total variation. This constitutes a geometric phenomenon which is in contrast to the situation on the positive real line (Kawazu and Watanabe, 1971) [8]. As an application we prove that the exponentially affine property of the Laplace transform carries over to the Fourier-Laplace transform if the diffusion coefficient is zero or invertible.

Original languageEnglish
Pages (from-to)3445-3459
Number of pages15
JournalStochastic Processes and their Applications
Volume122
Issue number10
DOIs
Publication statusPublished - Oct 2012
Externally publishedYes

Keywords

  • Affine processes
  • Jumps
  • Positive semidefinite processes
  • Wishart processes

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