Comparison results for reflected jump-diffusions in the orthant with variable reflection directions and stability applications. (English) Zbl 1190.60074

Piera, Francisco J.; Mazumdar, Ravi R.

Electron. J. Probab. 13, 1886-1908 (2008).

Summary: We consider reflected jump-diffusions in the orthant \(\mathbb R_+^n\) with time- and state-dependent drift, diffusion and jump-amplitude coefficients. Directions of reflection upon hitting boundary faces are also allow to depend on time and state. Pathwise comparison results for this class of processes are provided, as well as absolute continuity properties for their associated regulator processes responsible of keeping the respective diffusions in the orthant. An important role is played by the boundary property in that regulators do not charge times spent by the reflected diffusion at the intersection of two or more boundary faces. The comparison results are then applied to provide an ergodicity condition for the state-dependent reflection directions case.

MSC:

60J60	Diffusion processes
60J75	Jump processes (MSC2010)
60G17	Sample path properties
60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)
60H20	Stochastic integral equations

Keywords:

jump-diffusion processes; pathwise comparisons; state-dependent oblique reflection; Skorokhod maps; stability; ergodicity