Related papers: Systems with distributions and viability theorem
We study a class of singular stochastic control problems for a one-dimensional diffusion $X$ in which the performance criterion to be optimised depends explicitly on the running infimum $I$ (or supremum $S$) of the controlled process. We…
We study regularity properties of the dynamic value functions of primal and dual problems of optimal investing for utility functions defined on the whole real line. Relations between decomposition terms of value processes of primal and dual…
The main purpose of this paper is to establish the first and second order necessary optimality conditions for stochastic optimal controls using the classical variational analysis approach. The control system is governed by a stochastic…
We prove the solvability of It\^o stochastic equations with uniformly nondegenerate, bounded, measurable diffusion and drift in $L_{d+1}(\mathbb{R}^{d+1})$. Actually, the powers of summability of the drift in $x$ and $t$ could be different.…
This paper deals with the distributed order time-fractional diffusion equations with non-homogeneous Dirichlet (Nuemann) boundary condition. We first prove the wellposedness of the weak solution to the initial boundary value problem for the…
We consider a kind of stochastic exit time optimal control problems, in which the cost function is defined through a nonlinear backward stochastic differential equation. We study the regularity of the value function for such a control…
We study the two-times differentiability of the value functions of the primal and dual optimization problems that appear in the setting of expected utility maximization in incomplete markets. We also study the differentiability of the…
Solutions of the Dirichlet and Robin boundary value problems for the multi-term variable-distributed order diffusion equation are studied. A priori estimates for the corresponding differential and difference problems are obtained by using…
In this work, we propose some numerical schemes for linear kinetic equations in the diffusion and anomalous diffusion limit. When the equilibrium distribution function is a Maxwellian distribution, it is well known that for an appropriate…
We consider the decidability of state-to-state reachability in linear time-invariant control systems over continuous time. We analyse this problem with respect to the allowable control sets, which are assumed to be the image under a linear…
In this paper an iterated function system on the space of distribution functions is built. The inverse problem is introduced and studied by convex optimization problems. Some applications of this method to approximation of distribution…
We consider the nonlinear Schr\"{o}dinger equation $-\Delta u + V(x) u = \Gamma(x) |u|^{p-1}u$ in $\R^n$ where the spectrum of $-\Delta+V(x)$ is positive. In the case $n\geq 3$ we use variational methods to prove that for all $p\in…
Inverse problem to determine simultaneously a general space- and time-dependent source and an initial state in a fractional diffusion equation from an {\it a posteriori} measurement of the normal derivative of the state on a portion of a…
In this paper, we study a discrete-time stochastic optimal control problem under distribution uncertainty with convex control domain. By weak convergence method and Sion's minimax theorem, we obtain the variational inequality for cost…
This mini-course provides a presentation of the method of characteristics to initial/boundary-value problems for systems of first-order partial differential equations and to Hamilton-Jacobi variational inequalities. In particular, these…
We provide an overview on how to use the measurable selection techniques to derive the dynamic programming principle for a general stochastic optimal control/stopping problem. By considering its martingale problem formulation on the…
Motivated by the development and deployment of large-scale dynamical systems, often composed of geographically distributed smaller subsystems, we address the problem of verifying their controllability in a distributed manner. In this work…
We propose to solve a constrained distribution steering problem, i.e., steering a stochastic linear system from an initial distribution to some final, desired distribution subject to chance constraints. We do so by characterizing the…
Systems consisting of a single ordinary differential equation coupled with one reaction-diffusion equation in a bounded domain and with the Neumann boundary conditions are studied in the case of particular nonlinearities from the…
The problem of primary control of high-voltage direct current transmission systems is addressed in this paper, which contains four main contributions. First, to propose a new nonlinear, more realistic, model for the system suitable for…