2022/02/27 by Reddy, Anugu Sumith, Vivek S. Borkar, Borkar, Vivek S.
Economics, Econometrics and Finance · Mathematics · #34F05 #35D40 #35K65 #49L25 (Secondary) #60H10 (Primary) 60J25 #FOS: Mathematics #Mathematical Biology Tumor Growth #Nonlinear Partial Differential Equations #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2202.13382
openalex publication_date 2022/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we show that for the martingale problem for a class of degenerate diffusions with bounded continuous drift and diffusion coefficients, the small noise limit of non-degenerate approximations leads to a unique Feller limit. The proof uses the theory of viscosity solutions applied to the associated backward Kolmogorov equations. Under appropriate conditions on drift and diffusion coefficients, we will establish a comparison principle and a one-one correspondence between Feller solutions to the martingale problem and continuous viscosity solutions of the associated Kolmogorov equation. This work can be considered as an extension to the work of V. S. Borkar and K. S. Kumar (2010).