Penalty Method for Reflected Diffusions on the Half-Line

2015/09/06 by Bruggeman, Cameron, Sarantsev, Andrey
#60H10 #60J65 #FOS: Mathematics #Primary 60J60 #Probability (math.PR) #secondary 60J55

paper · doi:10.48550/arxiv.1509.01776

Abstract

Consider a reflected diffusion on the positive half-line. We approximate it by solutions of stochastic differential equations using the penalty method: We emulate the "hard barrier" of reflection by a "soft barrier" of a large drift coefficient, which compells the diffusion to return to the positive half-line. The main tool of the proof is convergence of scale functions.

Related

• Penalty Method for Obliquely Reflected Diffusions
• Boundary Approximation for Sticky Jump-Reflected Processes on the Half-Line
• Stochastic Homogenization of Reflected Diffusion Processes
• Weak and strong approximations of reflected diffusions via penalization methods
• Partially Reflected Diffusion