The Weak Convergence Limit Of A Kind Of Pure Death Process

In nature, we often meet Pure Death Process whose intuitive sense can be explained as below: some substance is constituted by some radioactive particles, whose life is a random variable that obeys index distribution withμas its parameter. And the partieles are independent of each other. Look from mierocosmic, the number of the radioaetive particles is a random variable. And look from macroscopic. The quality of the material which is constituted by the particles should obey the exponential decay, whose decay rate isμ. In fact, The quality of the material is mX, Assuming that the quality of a particle is m. And when m→0 and mX0=M, Then mXt should converges to an index funetion. In this paper I have proved that rule.What is interesting is that in a stock market, when the stocks which is hold in individuals is independent of each other, the amount of stocks (price) also obeys index attenuation rate. And its microscopic mechanism is also similar.