On strong solutions for positive definite jump-diffusions

Details On strong solutions for positive definite jump-diffusions On strong solutions for positive definite jump-diffusions

2009-10-09

arxiv.org/abs/0910.1784v5

Stochastic Processes and their Applications 121 (2011), No.9, pp. 2072-2086

Mathematics

Probability

version to appear in Stochastic Processes and Their Applications, 2011

Scientific paper

We show the existence of unique global strong solutions of a class of stochastic differential equations on the cone of symmetric positive definite matrices. Our result includes affine diffusion processes and therefore extends considerably the known statements concerning Wishart processes, which have recently been extensively employed in financial mathematics. Moreover, we consider stochastic differential equations where the diffusion coefficient is given by the alpha-th positive semidefinite power of the process itself with 0.5

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