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One of the definitions of stochastic continuity is: $\forall a > 0$ and $\forall s \geq 0$ $$\lim_{t\rightarrow s}\;P(|X(t)-X(s)|>a) = 0.$$ What does it mean intuitively? I know that it implies the jumps but am not sure how and why.

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    First try to intuitively understand stochastic convergence: http://en.wikipedia.org/wiki/Stochastic_convergence#Convergence_in_probability2010-10-11

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