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A new fundamental solution for a specific class of infinite dimensional Riccati equations is developed. This fundamental solution is based on the max-plus dual of the dynamic programming solution operator (or semigroup) of an associated control problem. By taking the max-plus dual of this semigroup operator, the kernel of a dual-space integral operator may be obtained. This kernel is the dual-space...
It is now well-known that many classes of deterministic control problems may be solved by max-plus or min plus (more generally, idempotent) numerical methods. The first such methods for stochastic control were developed only for discrete-time problems. The key tools enabling their development were the idempotent distributive property and the fact that certain solution forms are retained through application...
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