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

Eberhard Mayerhofer

Stochastic Processes and their Applications, 2012, vol. 122, issue 10, 3445-3459

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.

Keywords: Affine processes; Positive semidefinite processes; Jumps; Wishart processes (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (4)

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DOI: 10.1016/j.spa.2012.06.005

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