With a small probability the income is amplified by leverage N times. The income distribution becomes Asymptotically Substituting we find The two approaches are mathematically equivalent. In financial markets one observes periods with high volatility and enormous trading volumes interspersed with slow periods. In physical systems examples abound in heterogeneous systems with either Wide distribution of trap energies amorphous solds. Frozen disorder glasses.
Irregular flow fields hydrodynamics in heterogeneous media.
In the limit of an infinite lattice we then find the lattice Green's function Where BZ stands for Brillouin Zone. Started to discuss situations where individual processes in master equation were not Poisson distributed. Formulated continuous time random walk problem. Separated probability distribution after n steps from distribution after time t . The former distribution could be found by lattice Greens function methods.