Probability laws associated with a Kuhnian chain

2 Probability laws associated with a Kuhnian chain 

More generally, let us consider a Kuhnian chain of course S and (p + 1) points on the chain (excluding the extremities). Let s0,. . ., sp+1 be the courses of the chain segments connecting successive points (see Fig. 2.3). We have 

Here the vectors Uj are random variables and the parameters. The mean value is calculated by giving to r(s) all possible forms. 

In particular, we can consider the limit where the chain is infinite. To reach this limit, we shall make s0 and sp+1 become infinite, and therefore S will go to infinity. The new probability law reads  

The existence of an infinite chain is equivalent to the existence of the following limit 

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