Classical solutions of the Backward PIDE for a Marked Point Processes with characteristics modulated by a jump diffusion
Colaneri, Katia ; Frey, Rüdiger
arXiv, Tome 2019 (2019) no. 0, / Harvested from
The objective of this paper is to give conditions ensuring that the backward partial integro differential equation (PIDE) arising from a multidimensional jump-diffusion with a pure jump component has a classical solution, that is the solution is continuous, $\mathcal C^2$ in the diffusion component and $\mathcal{C}^1$ in time. Our proof uses a probabilistic arguments and extends the results of Pham (1998) to the case where the diffusion operator is not elliptic in all components and where the jump intensity is modulated by a diffusion process.
Publié le : 2019-03-18
Classification:  Mathematics - Probability 
@article{1903.07492,
     author = {Colaneri, Katia and Frey, R\"udiger},
     title = {Classical solutions of the Backward PIDE for a Marked Point Processes
  with characteristics modulated by a jump diffusion},
     journal = {arXiv},
     volume = {2019},
     number = {0},
     year = {2019},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1903.07492}
}

Colaneri, Katia; Frey, Rüdiger. Classical solutions of the Backward PIDE for a Marked Point Processes
  with characteristics modulated by a jump diffusion. arXiv, Tome 2019 (2019) no. 0, . http://gdmltest.u-ga.fr/item/1903.07492/