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Articles: 97
A Markov chain has a future conditional distribution depending on the present state alone.
Table of contents
2k
97
Birth-death chain
Markov chain
21
Product Markov chain
Markov chain
34
Transition matrix
Markov chain
11
Irreducible Markov chain
Markov chain
17
Aperiodic Markov chain
Markov chain
25
Recurrent state
Markov chain
14
Transient state
Markov chain
14
First return time
Markov chain
31
1
Mean recurrence time
First return time
21
Preservation under enlargement of transition support
Markov chain
55
Running minimum of an independent sequence is Markov
Markov chain
22
Overlapping moving sum need not be Markov
Markov chain
38
Reversible Markov chain
Markov chain
27
1
Detailed balance
Reversible Markov chain
15
Hitting probability
Markov chain
78
1
Harmonic hitting probability for the balanced-difference urn
Hitting probability
59
Expected hitting time
Markov chain
26
Expected occupation count before absorption
Markov chain
80
1
Four-state reflecting absorbing random walk
Expected occupation count before absorption
53
Conditional hitting time
Markov chain
23
Periodic Markov chain
Markov chain
18
Lazy Markov chain
Markov chain
14
Convergence to an invariant distribution
Markov chain
12
Recurrent Markov chain
Markov chain
79
4
Positive recurrent state
Recurrent Markov chain
13
Null recurrent state
Recurrent Markov chain
13
Recurrence criterion by return probabilities
Recurrent Markov chain
15
Biased random walk hitting probability
Recurrent Markov chain
23
Random walk on a graph
Markov chain
216
7
Simple random walk
Random walk on a graph
16
Simple random walk on the integer line
Random walk on a graph
90
2
Expected visits to the origin by a simple random walk
Simple random walk on the integer line
27
Simultaneous returns of independent simple random walks
Simple random walk on the integer line
38
Stationary distribution of a graph random walk
Random walk on a graph
12
Biased random walk
Random walk on a graph
84
1
Reflected biased random walk on the nonnegative integers
Biased random walk
73
Gambler's ruin
Markov chain
58
1
Expected duration of symmetric gambler's ruin
Gambler's ruin
42
Strong Markov property
Markov chain
71
1
Two-state excursion visit law
Strong Markov property
42
Stationary cycle occupation formula
Markov chain
41
Markov property
Markov chain
18
Continuous-time Markov chain
Markov chain
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
Finite Markov chain
Markov chain
Communicating class
Markov chain
65
3
Communicating states
Communicating class
20
Closed communicating class
Communicating class
16
Transient communicating class
Communicating class
29
Stationary distribution
Markov chain
8
Ancestors
(5)
Probability theory
Probability and statistics
Area of mathematics
Mathematics
Home
Incoming links
(13)
Aperiodic Markov chain
Birth-death chain
Communicating states
Irreducible Markov chain
Kac's lemma
Mean recurrence time
Solution
Solution
Solution
Solution
Preservation under enlargement of transition support
Recurrent state
Transition matrix
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