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.
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.