Abstract Stochastic optimal principle leads to the resolution of a partial differential equation (PDE), namely Hamilton–Jacobi–Bellman (HJB) equation. In general, this cannot be solved analytically, thus numerical algorithms are only tools provide accurate approximations. The aims paper is introduce novel fitted finite volume method solve high dimensional degenerated HJB from stochastic control...

We study the temperature control problem for Langevin diffusions in context of non-convex optimization. The classical optimal such a is bang-bang type, which overly sensitive to errors. A remedy allow explore other values and hence smooth out control. accomplish this by stochastic relaxed formulation incorporating randomization regularizing its entropy. derive state-dependent, truncated exponen...

This research focuses on designing a min–max robust control based neural dynamic programming approach using class of continuous differential networks (DNNs). The proposed controller solves the optimization cost function that depends trajectories system with an uncertain mathematical model satisfying non-linear perturbed systems. formulation enables concerning bounded modelling uncertainties and...

in the present work, a hybrid of fourier transform and homotopy perturbation method is developed for solving the non-homogeneous partial differential equations with variable coefficients. the fourier transform is employed with combination of homotopy perturbation method (hpm), the so called fourier transform homotopy perturbation method (fthpm) to solve the partial differential equations. the c...

‎in this paper‎, ‎we present a novel approach for image selective smoothing by the evolution of two paired nonlinear‎ ‎partial differential equations‎. ‎the distribution coefficient in de-noising equation controls the speed of distribution‎, ‎and is‎ ‎determined by the edge-strength function‎. ‎in the previous works‎, ‎the edge-strength function depends on isotropic‎ ‎smoothing of the image‎, ‎...

in the present study an alternative model allows the extension of the debye-hückel theory (dht) considering time dependence explicitly. from the electro-quasistatic approach (eqs) done in earlier studies time dependent potentials are suitable to describe several phenomena especially conducting media as well as the behaviour of charged particles in arbitrary solutions acting as electrolytes.this...

in this paper, the goursat problem of a general form for a linear partial differential equation is investigated with the help of the riemann function method. some results are given concerning the existence and uniqueness for the solution of the suggested problem.

We determine the optimal dynamic investment policy for a mean quadratic variation objective function by numerical solution of a nonlinear Hamilton-Jacobi-Bellman (HJB) partial differential equation (PDE). We compare the efficient frontiers and optimal investment policies for three mean variance like strategies: pre-commitment mean variance, time-consistent mean variance, and mean quadratic vari...

We study dynamic Bertrand mean field games (MFG) with exhaustible capacities in which companies compete with each other using the price as the strategic variable and the interaction among the competition is through the average price. We consider both continuum mean field games and finite player games. Dynamic continuum mean field games can be modeled as a system of partial differential equation...

• An extension of the deep Galerkin method (DGM) to solve Fokker–Planck PDEs keeping probability density constraints automatically satisfied. A novel application policy iteration algorithm (PIA) together with DGM HJB equations. Additional applications system coupled equations (arising from stochastic games) and mean-field Game PDE (coupled Fokker Planck). Both extensions are applicable multidim...