Necessary Conditions of Optimization for Partially Observed Controlled Diffusions

Likelihood based inference for observed and partially observed diffusions

This paper provides methods for carrying out likelihood based inference on non-linear observed and partially observed non-linear diffusions. The diffusions can potentially be non-stationary. The methods are based on innovative Markov chain Monte Carlo methods combined with an augmentation strategy. We study the performance of the methods as the degree of augmentation goes to infinity and find t...

Impulse Control of Multidimensional Jump Diffusions

This paper studies regularity properties of the value function for an infinite-horizon discounted cost impulse control problem, where the underlying controlled process is a multidimensional jump diffusion with possibly ‘infinite-activity’ jumps. Surprisingly, despite these jumps, we obtain the same degree of regularity as for the diffusion case, at least when the jump satisfies certain integrab...

AFRL-AFOSR-VA-TR-2017-0028 Dynamic Decision Making under Uncertainty and Partial Information

The researchers made significant progress in all of the proposed research areas. The first major task in the proposal involved duality in stochastic control and optimal stopping. In support of this task, the researchers developed new methods for efficiently solving optimal stopping problems of partially observable Markov processes and optimal stopping problems under jump-diffusion processes. Th...

Some Results on Necessary Conditions for Tow Quasidifferentiable Optimization Problems

A Correction to "A Relative Value Iteration Algorithm for Nondegenerate Controlled Diffusions"

In A Relative Value Iteration Algorithm for Nondegenerate Controlled Diffusions, [SIAM J. Control Optim., 50 (2012), pp. 1886–1902], convergence of the relative value iteration for the ergodic control problem for a nondegenerate diffusion controlled through its drift was established, under the assumption of geometric ergodicity, using two methods: (a) the theory of monotone dynamical systems an...