Time optimal control problems for systems with impulsive controls are investigated. Sufficient conditions for the existence of time optimal controls are given. A dynamical programming principle is derived and Lipschitz continuity of an appropriately defined value functional is established. The value functional satisfies a Hamilton-Jacobi-Bellman equation in the viscosity sense. A numerical exam...

We provide a dynamic programming principle for stochastic optimal control problems with expectation constraints. A weak formulation, using test functions and a probabilistic relaxation of the constraint, avoids restrictions related to a measurable selection but still implies the Hamilton-Jacobi-Bellman equation in the viscosity sense. We treat open state constraints as a special case of expecta...

* First and Preliminary Version! " ...The way out lay just in the possibility of attributing to the Hamilton principle, also, the operation of a wave mechanism on which the point-mechanical processes are essentially based, just as one had long become accustomed to doing in the case of phenomena relating to light and of the Fermat principle which governs them. Admittedly, the individual path of ...

We show how a minimal deformation of the geometry of the classical Hamilton-Jacobi equation provides a probabilistic theory whose cornerstone is the Hamilton-Jacobi-Bellman equation. This is the basis for a novel dynamical system approach to Stochastic Analysis. 1. Stochastic deformation of classical dynamical systems. The geometrical study of the Hamilton-Jacobi theory lies at the heart of Ana...

We consider the possible concentration in phase space of a sequence of eigenfunctions (or, more generally, a quasimode) of an operator whose principal symbol has completely integrable Hamilton flow. The semiclassical wavefront set WFh of such a sequence is invariant under the Hamilton flow. In principle this may allow concentration of WFh along a single closed orbit if all frequencies of the fl...

We study a non-local parabolic Lotka-Volterra type equation describing a population structured by a space variable x ∈ R and a phenotypical trait θ ∈ Θ. Considering diffusion, mutations and space-local competition between the individuals, we analyze the asymptotic (long– time/long–range in the x variable) exponential behavior of the solutions. Using some kind of real phase WKB ansatz, we prove ...

This paper discusses some of the modal involvements of analytical mechanics. I rst review the elementary aspects of the Lagrangian, Hamiltonian and Hamilton-Jacobi approaches. I then discuss two modal involvements; both are related to David Lewis' work on modality, especially on counterfactuals. The rst is the way Hamilton-Jacobi theory uses ensembles, i.e. sets of possible initial conditions. ...

We investigate the effect of noncommutativity and quantum corrections to temperature entropy a BTZ black hole based on Lorentzian distribution with generalized uncertainty principle (GUP). To determine Hawking radiation in tunneling formalism, we apply Hamilton-Jacobi method by using Wentzel-Kramers-Brillouin (WKB) approach. In present study, have obtained logarithmic due GUP. also address issu...