Suppose there is a system which behaves as follows. At time t = 0, there is a single particle, which we refer to as belo
Posted: Wed May 04, 2022 12:17 pm
Suppose there is a system which behaves as follows. At time t =
0, there is a single particle, which we refer to as belonging to
generation 0. This particle has an exp (1) clock. After the clock
expires, the particle disintegrates and 2 new particles are
created. Each of these particles has their own exp (1) clock.
Whenever, either of these particle's clock's go off, that particle
splits into two new particles, each of which gets its own new exp
(1) clock. However, the other particles do not split at this time.
There are then 3 particles, and the process continues on and on in
this manner. For each t > 0, let X(t) denote the number of
particles which exist at time t. Model X = {X(t). t>0} as a
CTMC, specifying the underlying DTMC transition matrix, the
underlying rates, and the starting state.
0, there is a single particle, which we refer to as belonging to
generation 0. This particle has an exp (1) clock. After the clock
expires, the particle disintegrates and 2 new particles are
created. Each of these particles has their own exp (1) clock.
Whenever, either of these particle's clock's go off, that particle
splits into two new particles, each of which gets its own new exp
(1) clock. However, the other particles do not split at this time.
There are then 3 particles, and the process continues on and on in
this manner. For each t > 0, let X(t) denote the number of
particles which exist at time t. Model X = {X(t). t>0} as a
CTMC, specifying the underlying DTMC transition matrix, the
underlying rates, and the starting state.