Compactification methods in the control of degenerate diffusions: existence of an optimal control

Abstract

This paper concerns the control of a degenerate diffusion. We study the existence of an optimal control for a diffusion which is the solution of the equation [d] where b and σ are continuous functions and u i, is the control, for a reward of the form J(r,z,u,) = E ∫T r h(s,x,us,ds+g(x T)We do not need the non-degenerate assumption on σ. We prove the existence of an optimal Markovian relaxed control,i.e. a control which takes values in the space of probability measures on a compact space A. We extend our results to the case of Borelian coefficients, with a supplementary hypothesis, and to the case of diffusions sigh jumps

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 231 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.