We consider a renewal jump diffusion process, more specifically a renewal insurance risk model with investments in a stock whose price is modeled by a geometric Brownian motion. Using Laplace transforms and regular variation theory, we introduce a transparent and unifying analytic method for investigating the asymptotic behavior of ruin...
Accelerated release of carbon from soils is one
of the most important feedbacks related to anthropogenically
induced climate change. Studies addressing the mechanisms
for soil carbon release through organic matter decomposition
have focused on the effect of changes in the average temperature,
with little attention to changes in temperature variability....
Advective skew dispersion is a natural Markov process defined ned
by a di ffusion with drift across an interface of jump discontinuity in
a piecewise constant diff usion coeffcient. In the absence of drift this
process may be represented as a function of -skew Brownian motion
for a uniquely determined...