Controlled Diffusion Processes

Abstract

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Bayesian Switching Multiple Disorder Problems

“…Since such free-boundary problems cannot normally be solved explicitly, the existence and uniqueness of classical as well as viscosity solutions of the variational inequalities, arising in the context of optimal stopping problems, have been extensively studied in the literature (see, e.g. Friedman [17], Bensoussan and Lions [9], Krylov [24], or Øksendal [26] can be verified by virtue of the regularity of the coefficients of the three-dimensional diffusion process, the application of these classical results would still have rather inexplicit character.…”

Controlled diffusions with boundary-crossing costs

“…The results of [4], Ch. IV, Section 4.3, also imply that if X(') is the solution to (1.1) under u(1), then…”

“…Another straightforward application of Krylov's extension of the Ito formula yields (see, e.g., [4], pp. 122)…”

“…As in [4], Section 2.6, we construct a family of Rn-valued diffusions X 8 , O<s<1, with X 8 (O) = x for all E, having drift coefficients mg:Rn _-R n and diffusion coefficients 0 8:Rn ->R nx n resp. such that (i) mi, ao are smooth and bounded with the same bounds as m,a resp., Proof.…”

“…This functional is often the time integral up to a stopping time of a 'running cost' function on the state space [1], [4].…”