  In this paper, we propose a stochastic dynamic model for earthquake rupture
and suggest that the Langevin equation of frictions may be used for
interpreting the slip distributions of rupture processes in earthquakes. The
steady-state solution of the derived Langevin equation analytically attains the
truncated exponential (TEX) distribution that is empirically characterized in
many rupture models of earthquake events worldwide, as demonstrated by
Thingbaijam and Mai (2016, https://doi.org/10.1785/0120150291). Our proposed
stochastic dynamic faulting model for earthquake rupture intrinsically includes
fluctuations and uncertainties in the heterogeneity of faulting planes as
random variables. Specifically, we related the characteristic parameter u_c in
TEX functions to the ratio of diffusion and friction coefficients D and \gamma
of the Langevin equation.
