Journal of Applied Probability: Volume 32 -

General necessary conditions for partially observed optimal stochastic controls
Part of:
Xunjing Li, Shanjian Tang
Published online by Cambridge University Press:

14 July 2016, pp. 1118-1137
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The partially observed control problem is considered for stochastic processes with control entering into the diffusion and the observation. The maximum principle is proved for the partially observable optimal control. A pure probabilistic approach is used, and the adjoint processes are characterized as solutions of related backward stochastic differential equations in finite-dimensional spaces. Most of the derivation is identified with that of the completely observable case.

On a conjecture for the non-existence of the expectation of randomly stopped sums
Part of:
- Stochastic processes
Claude Lefèvre, Sergey Utev
Published online by Cambridge University Press:

14 July 2016, pp. 1138-1141
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In a recent paper on the validity of Wald's equation, Roters (1994) raised an important question on the non-existence of the expectation of randomly stopped sums. The purpose of this note is to answer the question in the affirmative. As a consequence, an old question by Taylor (1972) also gets a positive answer.

Journal of Applied Probability