O-reflective Wall And The Number Of Features To Be Flying Wall Of The Birth And Death Process

The birth and death process is an importent denumerable Markov process. Given birth and death Q matrix Q - (qij),i, j E = {0,1,2...}, That is, qij = 0(| i-j| > 1),qii+1 = bi > 0(i 0),gii-1 = ai > 0(i > 0),gii = -(ai + bi)(i 0,a0 = a 0). The state 0 has four cases:(1) 0 is called reflecting barrier, if a0 = 0, b0 > 0. (2) 0 is called absorbing barrier, if a0 = 0,b0 = 0. (3) 0 is called leap-reflecting barrier, if a0 > 0,b0 = 0. (4) 0 is called quasi-leap-reflecting barrier, if a0 > 6, bo = 0. We denote a = a0 and Qa = Q implies the dependence of Q matrix on a. The characteristic numbers and their probability meaning of the birth and death process have been settled by both professor Yang in [1] and professor Wang in [2]. Professor Wang has adopted a method that solving difference equation in [2]. The characteristic numbers and their probability meaning of the birth and death process with zero as its quasi-leap-reflecting barrier have been partially settled by professor Yang in [1], which depends on setting up a method that solving system of liner equations with two boundaries.In this thesis , the author has setted up another method that solving system of liner equations with one boundary on the basis of the former method , and has improved further the characteristic numbers and their probability meaning of the birth and death process with zero as its quasi-leap-reflectingbarrier. Now, we have settled the characteristic numbers and their probability meaning of the birth and death process with zero as its two barriers. The main results are calculated as follows: 1.The probability of getting from k to j before explosion:2.The expected time process with as its left limit of the first leapping time getting from i to n before explosion:3. The expected time process with 0 as its left limit of the first leap-ping time getting from i to n before explosion:4.The expected time getting from i to n before 0 and explosion:5. The expected time getting from i to n before explosion:6. The expected time process with 0 as its left limit of the first leap-ping time getting from i to oo before explosion:7.The expected time process with oo as its left limit of the first leapping time getting from k to i - I before explosion:8. The expected time process with 0 as its left limit of the first leap-ping time getting from k to i - 1 before explosion:9. The expected time getting from k to i - I before explosion:10.The characteristic numbers and their probability meaning of mia , Nia , Ra, eia,etc.11.Ra < is equivalent to...