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Oct 8, 2017 at 6:29 comment added John Dawkins One analog of Levy's characterization of Brownian motion is due to S. Watanabe: if $\{N_t, t\ge 0\}$, is a counting process (right continuous pure jump process with jumps of size $+1$ only) with $N_t=0$ and if $N_t-\lambda t$ a martingale (for some $\lambda>0$) then $\{N_t, t\ge 0\}$ is a rate-$\lambda$ Poisson process.
Sep 28, 2017 at 9:34 vote accept Erfan Salavati
Sep 28, 2017 at 9:09 answer added Mateusz Kwaśnicki timeline score: 1
Sep 28, 2017 at 8:56 history asked Erfan Salavati CC BY-SA 3.0