Ok, let say we use the inverse transform method to generate the random variate from continuous distribution. So, the algorithm to do so is given as follows:

1. Generate U from U(0,1).

2. X \leftarrow F_{x}^{-1}(U)

3. Deliver X.

In this context, i believe the \leftarrow means equal i.e. we let X equal inverse function of U.

But, for a further example, i'm not sure if the \leftarrow use in this book (there is no notation section for the book anyway) really mean equal. Let's look at the following example of generating random variate from discrete variable using (still) the inverse transform method:

1.C \leftarrow P_0

2.B \leftarrow C

3.K \leftarrow 0

4.Generate U from U(0,1)

5.If U<=B (U<=g_k), deliver X=x_k

6.K \leftarrow K+1

7.C \leftarrow A_{k+1}C (P_{k+1}=A_{k+1}P_k)

8.B \leftarrow B+C (g_{k+1}=g_k+P{k+1})

9.Go to step 5.

I guess the leftarrow in all these means equal, but rather than using the usual equal sign i.e. '=' , we use the \leftarrow symbol to denote that this value keep changing due to the looping process executed here. That's my assumption. Please advise me if there is any reference about the symbol meaning here i.e. please let me know if there is any 'global' / general meaning to this symbol. I'm a little bit confused since this is my first time seeing this \leftarrow symbol.