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Can someone please help me to clarify a definition. I am reading about stochastic process from a book and I come across the statement: "martingales null at zero". What does this mean?

Please be a little elaborate with your answer.

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Martingale $(M_t)$ such that $P(M_0=0)=1$. – Did Jul 15 '11 at 19:17
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Nothing very interesting. In general, to say that a stochastic process $x(t)$ is "null at zero" means that, though at $t>0$ the values of $x(t)$ are random, at $t=0$ (the "start time") you know/specify that its value is fixed at zero: $x(0)=0$ (or, more formally, that $Prob(x(0)=0) = 1$. The typical example is the (most basic) random walk process.

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