Suppose we have a sequence f[i]. For example, it's
4 5 6 5 6 4 5 6 7 8 9 10 11 10 11 11 12 11 10 9 7 6 4 5 4 5 4
It is rather long and not directly storable in memory, so intead we store just statistics of values and deltas:
vals: 4 5 6 5 6 4 5 6 7 8 9 10 11 10 11 11 12 11 10 9 7 6 4 5 4 5 4
2
3
4 ****
5 *****
6 ****
7 **
8 *
9 **
10 ***
11 ****
12 *
13
deltas: 1 1 -1 1 -2 1 1 1 1 1 1 1 -1 1 0 1 -1 -1 -1 -2 -1 -2 1 -1 1 -1
-3
-2 ***
-1 ********
0 *
+1 **************
+2
How do I, having only histograms of values and deltas obtain a sample of random sequence with similar characteristics? Examples of such sequences are 11 10 11 10 8 7 5 4 5 4 5 6 7 8 9 10 11 10 11 or 6 4 5 5 4 5 6 7 8 9 10 11 10 11 9 7 8 9 10 11 - two humps in value distribution, mostly -2, -1 and +1 in delta distribution.
How is this problem formuated in proper mathematical terms?