Strassen-type law of the iterated logarithm for Brownian sheets presented by Pyke [7] is proved by using recent results of Kuelbs and Lepage [4]: the law of the iterated logarithm for Brownian motion in a Banach space and some applications are given.

Kerridge introduced a measure known as inaccuracy for complete probability distributions which is the generalisation of Shannon's entropy. In this paper we study a grouping property of the inaccuracy. Also we have established a coding theorem for personal codes by considering inaccuracy of order a and generalised mean length of order t under the condition .

Simple bounds on service level and turnover velocity are obtained for a periodic-review inventory system with a stationary order-up-to-level stocking policy and no backordering. Exact computational formulas are given for Poisson demand. An illustrative numerical example is presented, and the application of these bounds to retail inventory analysis is discussed.

The water level in a reservoir is modelled as a controlled diffusion process on a compact interval of the real line. The problem is to control the water discharge rate so as to minimise the expected costs, which depend upon the histories of the water levels and release rates. The form of the optimal control is studied for two general classes of reservoir control problems.