Stochastic Differential Equation on Extinction Probability

Agba M. E, Ugbebor O. O.

Abstract: This study was designed to develop and apply a stochastic differential equation that proves and computes the probability of extinction of a giving family using factorization method. This method was used on the stochastic birth-death process equation to determine the probability generating function. The limiting values of the generating function G (t, z) as t, z = 0 were taken to determine the extinction probability. Forty (40) families were studied and purposefully administered ( by one-on-one interaction) to heads of families using the ten (10) wards in Bekwarra Local Government Area, Cross River State to ascertain the birth rate, date rate and extinction probability.

Keywords: Extinction probability, Stochastic differential equation, Birth-death process