title: Multiplicative jump processes and applications to leaching of salt and contaminants in the soil.
abstract: We consider simple systems driven multiplicatively by white shot noise, which appear in the modeling of the dynamics of soil nutrients and contaminants. The dynamics of these systems is analyzed in two ways: solving a hierarchy of linear ordinary differential equations for the moments, which gives a time scale of convergence of the stationary probability density function; and characterizing the crossing properties, such as the mean first-passage time and the mean frequency of level crossing. These results are readily applicable to the study of geophysical systems, such as the problem of accumulation of salt in the root zone, i.e., soil salinization.
authors.affiliation: Department of Civil and Environmental Engineering, Duke University, Durham, North Carolina 27708, USA.
authors.forename: Yair
authors.initials: Y
authors.lastname: Mau
authors.affiliation: Department of Civil and Environmental Engineering, Duke University, Durham, North Carolina 27708, USA.
authors.forename: Xue
authors.initials: X
authors.lastname: Feng
authors.affiliation: Department of Civil and Environmental Engineering, Duke University, Durham, North Carolina 27708, USA.
authors.forename: Amilcare
authors.initials: A
authors.lastname: Porporato