Abstract
We formulate a stochastic control problem with a general information structure, and show that an optimal law exists and is characterized as the unique solution of a recursive stochastic equation. For a special information structure of the "signal-plus-noise" type and with quadratic cost-functions, this recursive equation is solved for the value function of the control problem. This value function is then shown to satisfy the Mortensen equation of Dynamic Programming in function-space.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 217-239 |
| Number of pages | 23 |
| Journal | Applied Mathematics and Optimization |
| Volume | 49 |
| Issue number | 3 |
| DOIs | |
| State | Published - May 2004 |
All Science Journal Classification (ASJC) codes
- Control and Optimization
- Applied Mathematics
Keywords
- Filtering
- Komlós theorem
- Mortensen equation
- Partial observations
- Recursive stochastic equations
- Stochastic control
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