Stochastic Processes

                                stochastic process
                                /     \          \
                               /       \           \
                              /         \            \
                             /           \             \
                   continuous time    random walk       Gaussian process
                        |                |                   /   |       \
                        |                |                 /     |         \
                        |             L�vy flight        /       |           \
                        |                              /         |             \
                 Lévy process                        /     Brownian bridge     Ornstein-Uhlenbeck process
              stationary increments                /    increments are not        mean-reverting
            independent increments               /        independent           stationary process
             /               \                 /
            /                  \             /
           /                     \         /
  Poisson process              Wiener process
                              (Brownian motion)





                            stochastic process
                                    |
                                    |
                            independent increments
                                    |
                                    |
                              Markov process
                                /   |     \
                               /    |       \
                             /      |         \
                           /        |           \
                Lévy flight   Wiener process     Poisson process



       stochastic process
             /  \
            /    \
           /      \
          /        \
submartingale     supermartingale
          \        /
           \      /
            \    /
             \ /
          martingale


Brownian motion is a martingale, a Markov process, a Gaussian process, a diffusion, a Lévy process.