Stochastic exit time problems arising in process control

On the Continuity of Stochastic Exit Time Control Problems

We determine a weaker sufficient condition than that of Theorem 5.2.1 in Fleming and Soner (2006) for the continuity of the value functions of stochastic exit time control problems.

A Strong Comparison Result for the Bellman Equation Arising in Stochastic Exit Time Control Problems and Its Applications

On a PDE Arising in One-Dimensional Stochastic Control Problems

The paper provides a systematic way for finding a partial differential equation that directly characterizes the optimal control, in the framework of one–dimensional stochastic control problems of Mayer type, with no constraints on the controls. The results obtained are applied to continuous–time portfolio problems.

A Method to Calculate the Exit Time in Stochastic Simulations

A novel method is presented to compute the exit time for the stochastic simulation algorithm. The method is based on the addition of a series of random variables and is derived using the convolution theorem. The final distribution is derived and approximated in the frequency domain. The distribution for the final time is transformed back to the real domain and can be sampled from in a simulatio...

On adaptive control problems of continuous-time stochastic systems

Let x = (xt)t≥0 be a scalar observed process with control u = (ut)t≥0 described by the stochastic differential equation dxt = θxtdt + utdt + dwt, t ≥ 0, driven by the standard Wiener process (wt)t≥0. Assume the parameter θ to be unknown. The problem solved in this paper is to approximate the process x to the stable Ornstein-Uhlenbeck process x = (xt )t≥0 with the given dynamic parameter a < 0, ...