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The purpose of this paper is to describe explicitly the solution for linear control systems on Lie groups. In case of linear control systems with inner derivations, the solution is given basically by the product of the exponential of the…
An optimal control problem with a time-parameter is considered. The functional to be optimized includes the maximum over time-horizon reached by a function of the state variable, and so an $L^\infty$-term. In addition to the classical…
Even in the face of deteriorating and highly volatile demand, firms often invest in, rather than discard, aging technologies. In order to study this phenomenon, we model the firm's profit stream as a Brownian motion with negative drift. At…
We study optimal control of Markov processes with age-dependent transition rates. The control policy is chosen continuously over time based on the state of the process and its age. We study infinite horizon discounted cost and infinite…
Stochastic optimal control problems have a long tradition in applied probability, with the questions addressed being of high relevance in a multitude of fields. Even though theoretical solutions are well understood in many scenarios, their…
We show that the minimum effort control of colloidal self-assembly can be naturally formulated in the order-parameter space as a generalized Schr\"{o}dinger bridge problem -- a class of fixed-horizon stochastic optimal control problems that…
In this work a simple method to enforce the positivity-preserving property for general high-order conservative schemes is proposed. The method keeps the original scheme unchanged and detects critical numerical fluxes which may lead to…
We revisit the classical singular control problem of minimizing running and controlling costs. The problem arises in inventory control, as well as in healthcare management and mathematical finance. Existing studies have shown the optimality…
An optimal control of a steady state thermistor problem is considered, where the convective boundary coefficient is taken as the control variable. A distinctive feature of this paper is that the problem is considered in arbitrary…
For a control Cauchy problem $$\dot x= {f}(t,x,u,v) +\sum_{\alpha=1}^m g_\alpha(x) \dot u_\alpha,\quad x(a)=\bar x, $$ on an interval $[a,b]$, we propose a notion of limit solution $x,$ verifying the following properties: i) $x$ is defined…
We construct a general stochastic process and prove weak convergence results. It is scaled in space and through the parameters of its distribution. We show that our simplified scaling is equivalent to time scaling used frequently. The…
In this paper, we study an approximation scheme for L\'evy processes with drift in terms of a representation that is akin to the celebrated Mehler formula for L\'evy-Ornstein-Uhlenbeck processes. The approximation scheme is based on a…
We consider optimal control problem with an integral cost which is a mean of a given function. As a particular case, the cost concerned is the Ces\`aro average. The limit of the value with Ces\`aro mean when the horizon tends to infinity is…
We consider a L\'evy process that starts from $x<0$ and conditioned on having a positive maximum. When Cram\'er's condition holds, we provide two weak limit theorems as $x\to -\infty$ for the law of the (two-sided) path shifted at the first…
The first motivation of our paper is to explore further the idea that, in risk control problems, it may be profitable to base decisions both on the position of the underlying process Xt and on its supremum Xt := sup 0$\le$s$\le$t Xs.…
We study optimal investment in an asset subject to risk of default for investors that rely on different levels of information. The price dynamics can include noises both from a Wiener process and a Poisson random measure with infinite…
We study a discounted singular stochastic control problem driven by a general L\'evy process, where the objective is to minimize a cost functional composed of a running cost and a control cost that depends on the current state of the…
This paper investigates the data-driven predictive control problems for a class of continuous-time industrial processes with completely unknown dynamics. The proposed approach employs the data-driven technique to get the system matrices…
We consider a production-inventory control model with finite capacity and two different production rates, assuming that the cumulative process of customer demand is given by a compound Poisson process. It is possible at any time to switch…
We have shown recently that a Markov process conditioned on rare events involving time-integrated random variables can be described in the long-time limit by an effective Markov process, called the driven process, which is given…