an:06868374
Zbl 1390.60277
Kr??hner, Paul; Larsson, Martin
Affine processes with compact state space
EN
Electron. J. Probab. 23, Paper No. 29, 23 p. (2018).
00389136
2018
j
60J25 60J27 60J75
affine processes; compact state space; Markov chains
Summary: The behavior of affine processes, which are ubiquitous in a wide range of applications, depends crucially on the choice of state space. We study the case where the state space is compact, and prove in particular that (i) no diffusion is possible; (ii) jumps are possible and enforce a grid-like structure of the state space; (iii) jump components can feed into drift components, but not vice versa. Using our main structural theorem, we classify all bivariate affine processes with compact state space. Unlike the classical case, the characteristic function of an affine process with compact state space may vanish, even in very simple cases.