Define u in (4.14) as where it is known, however, that ξ ≤ U = βa , a.s., for some finite β . For given β and a , can you find c such that (4.14) gives a better bound with this u than with the u used...

Define u in (4.14) as

where it is known, however, that ξ ≤ U = βa , a.s., for some finite β . For given β and a , can you find c such that (4.14) gives a better bound with this u than with the u used to obtain (4.3)?