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Mathematical and computational approaches for stochastic control of river environment and ecology from fisheries viewpoint

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Document pages: 33 pages

Abstract: We present a modern stochastic control framework for dynamic optimization ofriver environment and ecology. We focus on a fisheries problem in Japan, andshow several examples of simplified optimal control problems of stochasticdifferential equations modeling fishery resource dynamics, reservoir waterbalance dynamics, benthic algae dynamics, and sediment storage dynamics. Theseproblems concern different phenomena with each other, but they all reduce tosolving degenerate parabolic or elliptic equations. Optimal controls and valuefunctions of these problems are computed using finite difference schemes.Finally, we present a higher-dimensional problem of controlling a dam-reservoirsystem using a semi-Lagrangian discretization on sparse grids. Our contributionshows the state-of-art of modeling, analysis, and computation of stochasticcontrol in environmental engineering and science, and related research areas.

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