Avoiding the origin: A finite-fuel stochastic control problem

Avoiding the Origin: a Finite-fuel Stochastic Control Problem

We consider a model for the control of a satellite—fuel is expended in a linear fashion to move a satellite following a diffusion—the aim is to keep the satellite above a critical level. Under suitable assumptions on the drift and diffusion co-efficients, it is shown that the probability of the satellite falling below the critical level is minimised by a policy which moves the satellite a certa...

Avoiding the boson sign problem at finite chemical potential

The usual path integral formulation for scalar particles at finite density involves a sign problem, making numerical simulation impractical. We present alternative methods free of this difficulty. We apply these approaches to |φ | 4 theory in 2 + 1 dimensions, presenting preliminary numerical results for physical quantities in the vicinity of the phase transition in the T − µ plane.

Finite-fuel Singular Control with Discretionary Stopping

We discuss the finite-fuel, singular stochastic control problem of optimally tracking the standard Brownian motion x+W (·) started at x ∈ IR, by an adapted process ξ(·) = ξ+(·)−ξ−(·) of bounded total variation ξ̌(t) = ξ+(t) + ξ−(t) ≤ y, ∀ 0 ≤ t < ∞, so as to minimize the total expected discounted cost

Approximation of a Stochastic Ergodic Control Problem

We study a degenerate non linear optimal stochastic control problem of ergodic type. We rst prove that for each feedback control law, there exists a unique invariant measure which is equivalent to Lebesgue measure. This is proved using an accessibility property of the stochastic diierential equation, after the discontinuous part of the drift has been removed via a change of probability measure....

A stochastic control problem for SNLPs