List of Figures
| 1.1 | Symmetric nearest-neighbor random walk on regular planar triangular network. |
| 1.2 | Gambler's ruin. Gambler A finishes the game at time  with a gain of  units starting from a fortune of  units. The successive states of his fortune are represented by the • and joined by dashes. The arrows on the vertical axis give his probabilities of winning or losing at each toss. |
| 1.3 | Branching process. (b) The genealogical tree for a population during six generations; • represent individuals and dashed lines their parental relations. (a) The vertical axis gives the numbers  of the generations, of which the sizes figure on its right. (c) The table underneath the horizontal axis gives the  for  and  , of which the sum over  yields  . |
| 1.4 | The Ehrenfest Urn. Shown at an instant when a particle transits from the right compartment to the left one. The choice of the particle that changes compartment at each step is uniform. |
| 1.5 | Renewal process. The • represent the ages at the discrete instants on the horizontal axis and are linearly interpolated by dashes in their increasing phases. Then,  if  . The  represent the two possible ages at time  , which are  if  and  if  . |
| 1.6 | Search for the word GAG: Markov chain graph. The graph for the automaton is obtained by replacing  by “if the next term is  ,”  by “if the next term is  ,”  by “if the next term is not  ,” and  by “if the next term is neither  nor  .” |
| 1.7 | Product chain. The first and second coordinates are drawn independently according to  and  . |
| 2.1 | Strong Markov property. The successive states of  are represented by the filled circles and are linearly interpolated by dashed lines and  is a stopping time. |
| 2.2 | Successive hitting times of  and induced chain. The successive states of  are represented by the filled circles and are linearly interpolated, and  corresponds to the points between the two horizontal lines. We see  for  ,  , and  . |
| 2.3 | Graphical study of  with  . (Left)  , and the sequence converges to  . (Right)  , and the sequence converges to  , the unique fixed point of  other than  . |
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