ABSTRACT
{ X ( t ) , t ⩾ 0 } https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003067498/6ba0c26b-f086-40cc-86ed-1693dc596221/content/eq6366.tif"/> is called a generalized non-time-homogeneous Birth and Death process if it is a Markov process with continuous parameters, numerable states, and the transition probability p i , j ( s , t ) = P ( X ( t ) = j ∣ X ( s ) = i ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003067498/6ba0c26b-f086-40cc-86ed-1693dc596221/content/eq6367.tif"/> that satisfies () lim h → 0 + 1 h ( p i , j ( t , t + h ) − δ i j { α i ( t ) , j = i + 2 λ i ( t ) , j = i + 1 μ i ( t ) , j = i − 1 β i ( t ) , j = i − 2 − γ i ( t ) , j = i 0 , | j − i | > 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003067498/6ba0c26b-f086-40cc-86ed-1693dc596221/content/eq6368.tif"/>
