/ Independent Poisson Process / Infinitesimal Generator / Large Time Asymptotic Behavior / Large Time Asymptotics / linear diffusion equation / Markov processes analysis / MATHEMATICS / Applied / MATHEMATICS / Differential Equations / General / MATHEMATICS / General / MATHEMATICS / Probability & Statistics / Bayesian Analysis / MGF / Negative Half Line / nonlinear diffusion equations / nonlinear stochastic systems research / ordinary differential equation / Ordinary Stochastic Differential Equations / Parabolic Scaling / Poisson process / Positive Weak Solution / Probability & statistics / Probability and statistics / probability theory applications / Pure Jump Process / random walk theory / Riemann problem / Sample Path / statistical mechanics concepts / stochastic differential equations / Stochastic Integral / stochastic modeling methods / Stochastics