Perturbed backward stochastic differential equations

Janković, Svetlana; Jovanović, Miljana; Djordjević, Jasmina

doi:10.1016/j.mcm.2011.11.018

Cited by 9 publications

(11 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If we substitute estimate (13) in (12), and take E sup t∈[t 0 ,T] over whole inequality (12) we have…”

Section: Main Results and Their Proofsmentioning

confidence: 99%

“…Author by herself have dealt with different problems related to several type of backward differential equations. Problem of additive perturbations was considered by Janković, Jovanović and Ðordević in their paper [12] for nonhomogeneous BSDEs, and later on by Ðordević and Janković in [2] for Volterra BSDEs. Ðordević [5] proved the closeness result for the general type of perturbations for reflected BSDEs.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Some analytic approximations for backward stochastic differential equations

Ðordjevic

2020

Filomat

View full text Add to dashboard Cite

We consider an analytic iterative method to approximate the solution of the backward stochastic differential equation of general type. More precisely, we define a sequence of approximate equations and give sufficient conditions under which the approximate solutions converge with probability one and in pth moment sense, p ? 2, to the solution of the initial equation under Lipschitz condition. The Z-algorithm for this iterative method is introduced and some examples are presented to illustrate the theory.

show abstract

“…If we substitute estimate (13) in (12), and take E sup t∈[t 0 ,T] over whole inequality (12) we have…”

Section: Main Results and Their Proofsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Some analytic approximations for backward stochastic differential equations

Ðordjevic

2020

Filomat

View full text Add to dashboard Cite

show abstract

“…the problems are translated on more simple and familiar cases which are easier to solve and investigate (see [1][2][3] for example). Problem of additively perturbed backward stochastic differential equations is analysed by Janković, M. Jovanović, J. Ðorđević in [4], while generally perturbed reflected backward stochastic differential equations are already observed by Ðorđević and Janković in [5]. Topic of this chapter is additive type of perturbations for reflected backward stochastic differential equations as a special type of mention general problem for reflected backward stochastic differential equations, and a more general one than the additive perturbation problem for simple backward stochastic differential equations.…”

Section: Introductionmentioning

confidence: 98%

Effect of Additive Perturbations on the Solution of Reflected Backward Stochastic Differential Equations

Đorđević¹

2021

Recent Developments in the Solution of Nonlinear Differential Equations

View full text Add to dashboard Cite

This chapter has as a topic large class of general, nonlinear reflected backward stochastic differential equations with a lower barrier, whose generator, final condition as well as barrier process arbitrarily depend on a small parameter. The solutions of these equations which are obtained by additive perturbations, named the perturbed equations, are compared in the Lp-sense, p∈]1,2[, with the solutions of the appropriate equations of the equal type, independent of a small parameter and named the unperturbed equations. Conditions under which the solution of the unperturbed equation is Lp-stable are given. It is shown that for an arbitrary a>0 there exists ta≤T, such that the Lp-difference between the solutions of both the perturbed and unperturbed equations is less than a for every t∈taT.

show abstract

“…In the current contribution, we shall consider an ODE system with quasilinear nonnegative definite symmetric right-hand side (sometimes called degenerate parabolic system; see (5)). Such and similar type of equations have been intensively considered recently in both deterministic and stochastic setting (see [1] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Global Controllability for Quasilinear Non-negative Definite System of ODEs and SDEs

Djordjevic¹,

Konjik²,

Mitrović³

et al. 2021

Preprint

View full text Add to dashboard Cite

We consider exact and averaged control problem for a system of quasi-linear ODEs and SDEs with a non-negative definite symmetric matrix of the system. The strategy of the proof is the standard linearization of the system by fixing the function appearing in the nonlinear part of the system, and then applying the Leray-Schauder fixed point theorem.We shall also need the continuous induction arguments to prolong the control to the final state which is a novel approach in the field. This enables us to obtain controllability for arbitrarily large initial data (so called global controllability).

show abstract

Perturbed backward stochastic differential equations

Cited by 9 publications

References 20 publications

Some analytic approximations for backward stochastic differential equations

Some analytic approximations for backward stochastic differential equations

Effect of Additive Perturbations on the Solution of Reflected Backward Stochastic Differential Equations

Global Controllability for Quasilinear Non-negative Definite System of ODEs and SDEs

Contact Info

Product

Resources

About