Many microeconomic and engineering problems can be formulated as stochastic optimization problems that are modelled by ItÃ´ evolution systems and by cost functionals expressed as stochastic integrals.â€¦ (More)

In this paper, we introduce and explore some properties of two types of multitime partial differential equations, one as geometrical prolongation of the reaction-diffusionâ€¦ (More)

Geometric structure of global integral variational functionals on higher order tangent bundles and Grassmann fibrations are investigated. The theory of Lepage forms is extended to these structures.â€¦ (More)

Many science and engineering problems can be formulated as optimization problems that are governed by m-flow type PDEs (multitime evolution systems) and by cost functionals expressed as multipleâ€¦ (More)

Using parametrized curves (Section 1) or parametrized sheets (Section 3), and suitable metrics, we treat the jet bundle of order one as a semi-Riemann manifold. This point of view allows theâ€¦ (More)

Many science and engineering problems can be formulated as optimization problems that are governed by contact distributions (multitime Pfaff evolution systems) and by cost functionals expressed asâ€¦ (More)

In Â§1 the authors define the notion of harmonic map between two generalized Lagrange spaces. In Â§2 it is proved that for certain systems of differential or partial differential equations, theâ€¦ (More)

Many science and engineering problems can be formulated as optimization problems that are governed by m-flow type PDEs (multitime evolution systems) and by cost functionals expressed as curvilinearâ€¦ (More)

This paper introduces new types of Euler-Lagrange PDEs required by optimal control problems with performance criteria involving curvilinear or multiple integrals subject to evolutions ofâ€¦ (More)

This paper interrelates the performance criteria involving path independent curvilinear integrals, the multitime maximum principle, the multitime Hamilton-Jacobi-Bellman PDEs and the multitimeâ€¦ (More)