相关论文: Maximum principle for SPDEs and its applications
We provide sufficient conditions for the continuity of the free-boundary in a general class of finite-horizon optimal stopping problems arising for instance in finance and economics. The underlying process is a strong solution of one…
We establish the dual notions of scaling and saturation from geometric control theory in an infinite-dimensional setting. This generalization is applied to the low-mode control problem in a number of concrete nonlinear partial differential…
Discrete maximum principles in the approximation of partial differential equations are crucial for the preservation of qualitative properties of physical models. In this work we enforce the discrete maximum principle by performing a simple…
We present a novel approach to the proof of Peng's maximum principle for McKean-Vlasov stochastic differential equations (SDE). The main step is the introduction of a third adjoint equation, a conditional McKean-Vlasov backward SDE, to…
The main scope of this article is to define the concept of principal eigenvalue for fully non linear second order operators in bounded domains that are elliptic and homogenous. In particular we prove maximum and comparison principle, Holder…
A necessary maximum principle is proved for optimal controls of stochastic systems driven by multidimensional Teugel's martingales. The multidimensional Teugel's martingales are constructed by orthogonalizing the multidimensional L\'{e}vy…
In this paper we introduce a new technique to prove the existence of closed subspaces of maximal dimension inside sets of topological vector sequence spaces. The results we prove cover some sequence spaces not studied before in the context…
The maximality principle has been a valuable tool in identifying the free-boundary functions that are associated with the solutions to several optimal stopping problems involving one-dimensional time-homogeneous diffusions and their running…
It is shown that the formula for the M\"obius pseudodistance for the annulus yields better estimates than previously known for the constant in the Bergman space maximum principle. A maximum principle for the Fock space is proved.
In this paper, we consider the following non-linear equations in unbounded domains $\Omega$ with exterior Dirichlet condition: \begin{equation*}\begin{cases} (-\Delta)_p^s u(x)=f(u(x)), & x\in\Omega,\\ u(x)>0, &x\in\Omega,\\ u(x)\leq0,…
Dependence on the parameter is continuous when perturbations of the parameter preserves strict preference for one alternative over another. We characterise this property via a utility function over alternatives that depends continuously on…
Maximum entropy principle identifies forces conjugated to observables and the thermodynamic relations between them, independent upon their underlying mechanistic details. For data about state distributions or transition statistics, the…
We study the problem of computing the \textsc{Maxima} of a set of $n$ $d$-dimensional points. For dimensions 2 and 3, there are algorithms to solve the problem with order-oblivious instance-optimal running time. However, in higher…
Some optimization problems coming from the Differential Geometry, as for example, the minimal submanifolds problem and the harmonic maps problem are solved here via interior solutions of appropriate multitime optimal control problems.…
We consider an optimal control problem for a system of local continuity equations on a space of probability measures. Such systems can be viewed as macroscopic models of ensembles of non-interacting particles or homotypic individuals,…
We address a class of systems for which the solution to an H-infinity optimal control problem can be given on a very simple closed form. In fact, both the control law and optimal performance value are explicitly given. The class of systems…
We extend the Gibbs conditioning principle to an abstract setting combining infinitely many linear equality constraints and non-linear inequality constraints, which need not be convex. A conditional large large deviation principle (LDP) is…
In dimension $n=1$ we obtain $L^{p_1}(\mathbb R) \times\dots\times L^{p_m}(\mathbb R)$ to $L^p(\mathbb R)$ boundedness for the multilinear spherical maximal function in the largest possible open set of indices and we provide counterexamples…
Through the Maximum principle we define the principal eigenvalue for a class of fully-nonlinear operators that are the non-variational equivalent of the p-Laplacian. We also obtain some a priori Holder estimates for non-negative solutions…
In this paper we consider Hopf's Lemma and the Strong Maximum Principle for supersolutions to a class of non elliptic equations. In particular we prove a sufficient condition for the validity of Hopf's Lemma and of the Strong Maximum…