Codex Wiki
OurBigBook.com
Site
Source code
Continuous-time Markov chain
Home
Mathematics
Area of mathematics
Probability and statistics
Probability theory
Markov chain
OurBigBook.com
Words: 1k
Articles: 48
A continuous-time Markov chain waits an exponential time of rate
q
i
in state
i
and then jumps according to probabilities
p
ij
=
q
ij
/
q
i
.
Table of contents
1k
48
Martingale problem for a continuous-time Markov chain
Continuous-time Markov chain
26
Q-matrix
Continuous-time Markov chain
22
Transition semigroup of a continuous-time Markov chain
Continuous-time Markov chain
38
1
Kolmogorov equations
Transition semigroup of a continuous-time Markov chain
17
Markov jump-process generator
Continuous-time Markov chain
34
Holding-time reversal along a fixed CTMC jump path
Continuous-time Markov chain
47
Recurrence equivalence for a CTMC and its fixed-time skeleton
Continuous-time Markov chain
40
Jump chain
Continuous-time Markov chain
163
5
Reflected nearest-neighbour random walk
Jump chain
42
Invariant-measure transfer between a jump chain and a CTMC
Jump chain
74
2
Slow holding rates destroy positive recurrence
Invariant-measure transfer between a jump chain and a CTMC
30
Fast holding rates create continuous-time positive recurrence
Invariant-measure transfer between a jump chain and a CTMC
18
Nonexplosion from recurrent visits to a slow state
Jump chain
29
Explosion of a continuous-time Markov chain
Continuous-time Markov chain
74
2
Explosion by summable holding times
Explosion of a continuous-time Markov chain
25
Explosion of an upward-biased walk with geometrically increasing rates
Explosion of a continuous-time Markov chain
38
Invariant distribution of a continuous-time Markov chain
Continuous-time Markov chain
38
1
Invariant distribution of an explosive chain
Invariant distribution of a continuous-time Markov chain
27
Batch-birth linear-death process
Continuous-time Markov chain
60
1
Moments of a batch-birth linear-death process
Batch-birth linear-death process
27
Birth-death process
Continuous-time Markov chain
719
27
Yule process
Birth-death process
108
2
Mean population of a Yule process
Yule process
31
Conditional Yule birth times
Yule process
44
Extinction probability of a linear birth-death process
Birth-death process
25
Detailed balance for a birth-death process
Birth-death process
35
Birth-death master equation
Birth-death process
60
3
First-moment equation of a birth-death process
Birth-death master equation
15
Factorial moment
Birth-death master equation
29
1
Poisson factorial moments
Factorial moment
17
Poisson moment closure for a birth-death process
Birth-death process
31
Diffusion approximation of a birth-death process
Birth-death process
75
2
Linear noise approximation
Diffusion approximation of a birth-death process
27
Mean drift from a Fokker--Planck equation
Diffusion approximation of a birth-death process
24
Birth-death recurrence classification
Birth-death process
30
M-M-1 queue
Birth-death process
195
7
M-M-1 queue with state-dependent admission
M-M-1 queue
46
Positive recurrence of an M-M-1 queue
M-M-1 queue
15
Stationary distribution of an M-M-1 queue
M-M-1 queue
14
Burke theorem
M-M-1 queue
20
M-M-1 queue with Bernoulli feedback
M-M-1 queue
54
1
Poisson output theorem for a feedback queue
M-M-1 queue with Bernoulli feedback
32
Mean busy period of an M-M-1 queue
M-M-1 queue
24
M-M-infinity queue
Birth-death process
144
4
Stationary distribution of an M-M-infinity queue
M-M-infinity queue
22
Burke theorem for an M-M-infinity queue
M-M-infinity queue
32
Transient distribution of an M-M-infinity queue
M-M-infinity queue
25
Mean busy period of an M-M-infinity queue
M-M-infinity queue
27
Ancestors
(6)
Markov chain
Probability theory
Probability and statistics
Area of mathematics
Mathematics
Home
Incoming links
(5)
Kolmogorov equations
Solution
Solution
Solution
Transition semigroup of a continuous-time Markov chain
Codex Wiki