Markov Chains: Analytic and Monte Carlo Computations

Index

1. σ-field
   1. engendered
   2. generated
   3. product
2.  
3. a.s.
4. absorbing
5. algorithm
   1. Metropolis
   2. Propp-Wilson, see exact simulation
6. almost sure, almost surely, see a.s.
7. aperiodic, see period
8.  
9. birth and death, see chain
10. branching
11.  
12. canonical space, process
13. cemetery state
14. Chapman-Kolmogorov formula
15. class
    1. aperiodic
    2. closed irreducible
    3. recurrent
16. coalescence
17. communication
    1. Condition
    2. Doeblin condition
    3. Kolmogorov
       1. Condition
18. conditioning on the first step, see one step forward
19. convergence
    1. weak, in law
20. counting automaton, see word search
21. coupling
    1. Doeblin
    2. maximal
22. criterion
    1. Foster
    2. invariant law
    3. Lamperti
    4. potential matrix
    5. transience-recurrence
    6. Tweedie
23. curse of dimensionality
24.  
25. Dirichlet form
26. Dirichlet problem
27. distribution
    1. hitting
    2. stationary, see invariant law
28. dog-flea model, see Ehrenfest
29. Doob
30. duality
    1. Hilbert space
    2. measure-function
31.  
32. Ehrenfest
33. eigenspace, see spectrum
34. eigenvalues, see spectrum
35. enlarged state space, see cemetery state
36. entropy
37. equation
    1. detailed balance, see local balance
    2. equilibrium, see balance
    3. global balance
    4. heat
    5. local balance
    6. parabolic
    7. reversibility, see local balance
38. equilibrium
    1. thermodynamical
39. evolution of a population, see branching
40. exit time, distribution
41. exponential bounds
42.  
43. filtration
44. finite-dimensional marginals
    1. consistent
45. Fourier transform, discrete
46. function
    1. generating
    2. harmonic
    3. Lyapunov
    4. super- or sub-harmonic
47.  
48. Galton-Watson, see branching
49. gambler's ruin
50. global optimisation, see simulated annealing
51. graph
52.  
53. Hahn-Jordan decomposition
54.  
55. i.i.d. ...