Displaying similar documents to “Optimal control for absolutely continuous stochastic processes and the mass transportation problem.”

On near-optimal necessary and sufficient conditions for forward-backward stochastic systems with jumps, with applications to finance

Mokhtar Hafayed, Petr Veverka, Syed Abbas (2014)

Applications of Mathematics

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We establish necessary and sufficient conditions of near-optimality for nonlinear systems governed by forward-backward stochastic differential equations with controlled jump processes (FBSDEJs in short). The set of controls under consideration is necessarily convex. The proof of our result is based on Ekeland's variational principle and continuity in some sense of the state and adjoint processes with respect to the control variable. We prove that under an additional hypothesis, the near-maximum...

Multiscale convergence and reiterated homogenization of parabolic problems

Anders Holmbom, Nils Svanstedt, Niklas Wellander (2005)

Applications of Mathematics

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Reiterated homogenization is studied for divergence structure parabolic problems of the form ∂ u ε / ∂ t - div a x , x / ε , x / ε 2 , t , t / ε k ∇ u ε = f . It is shown that under standard assumptions on the function a ( x , y 1 , y 2 , t , τ ) the sequence { u ϵ } of solutions converges weakly in L 2 ( 0 , T ; H 0 1 ( Ω ) ) to the solution u of the homogenized problem ∂ u / ∂ t - div ( b ( x , t ) ∇ u ) = f .

Conjugacy criteria and principal solutions of self-adjoint differential equations

Ondřej Došlý, Jan Komenda (1995)

Archivum Mathematicum

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Oscillation properties of the self-adjoint, two term, differential equation ( - 1 ) n ( p ( x ) y ( n ) ) ( n ) + q ( x ) y = 0 ( * ) are investigated. Using the variational method and the concept of the principal system of solutions it is proved that (*) is conjugate on R = ( - ∞ , ∞ ) if there exist an integer m ∈ { 0 , 1 , ⋯ , n - 1 } and c 0 , ⋯ , c m ∈ R such that ∫ ∞ 0 x 2 ( n - m - 1 ) p - 1 ( x ) d x = ∞ = ∫ 0 ∞ x 2 ( n - m - 1 ) p - 1 ( x ) d x and lim sup x 1 ↓ - ∞ , x 2 ↑ ∞ ∫ x 1 x 2 q ( x ) ( c 0 + c 1 x + ⋯ + c m x m ) 2 d x ≤ 0 , q ( x ) ¬ ≡ 0 . Some extensions of this criterion are suggested.