deletions | additions       diff --git a/subsection_Approximation_of_probability_distribution__.tex b/subsection_Approximation_of_probability_distribution__.tex  index 0ecb05c..2703349 100644  --- a/subsection_Approximation_of_probability_distribution__.tex  +++ b/subsection_Approximation_of_probability_distribution__.tex 
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\[P_{hist}((x,y),T) = \sum_{(x',y')\in T}\mathbb{1}_{(x=x',y=y')}\]  Similarly the histogram of joint distribution of two trajectories $T$ and $S$ is given by:  \[P_{hist}((x_{1},y_{1},x_{2},y_{2}),TxS) \[P_{hist}((x_{1},y_{1},x_{2},y_{2}),T\times S)  = \sum_{(x'_{1},y'_{1},x'_{2},y'_{2})\in TxS}\mathbb{1}_{(x_{1}=x'_{1},y_{1}=y'_{1},x_{2}=x'_{2},y_{2}=y'_{2})}\] One can remark that the time parameter is here implicitly taking into account as we add contribution to $P_{hist}((x_{1},y_{1},x_{2},y_{2}),TxS)$ $P_{hist}((x_{1},y_{1},x_{2},y_{2}),T\times S)$  if and only if $T$ is in $(x_{1},y_{1})$ at the same time $S$ is in $(x_{2},y_{2})$.