Stochastic Differential Systems With Memory: Theory, Examples and Applications

Mohammed, Salah-Eldin A.

doi:10.1007/978-1-4612-2022-0_1

Cited by 132 publications

(142 citation statements)

References 36 publications

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“…We first introduce some notations and definitions which also used in [1,4,5,9]. Let C b be the Banach space of all bounded uniformly continuous functions Φ : C → R with the sup norm…”

Section: The Notions and Definitionsmentioning

confidence: 99%

“…Under the above assumptions, for any v(·) ∈ U ad , the control system (2.2) with the aftereffect has a unique strong solution {X s,ϕ;v (t), 0 ≤ s ≤ t ≤ T }, and also we have the following estimates by the existence and uniqueness theorem of SDDE in Mohammed [8,9]:…”

Section: Notations and Formulation Of The Problemmentioning

confidence: 99%

“…Such processes can be described by the stochastic differential delayed equation (SDDE). Many examples can be found in Mohammed [8,9]. Whereas the dynamic programming principle can also be extended to stochastic control problems with delay (see e.g.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic programming principle for stochastic recursive optimal control problem with delayed systems

Chen

2012

ESAIM: COCV

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Abstract.In this paper, we study one kind of stochastic recursive optimal control problem for the systems described by stochastic differential equations with delay (SDDE). In our framework, not only the dynamics of the systems but also the recursive utility depend on the past path segment of the state process in a general form. We give the dynamic programming principle for this kind of optimal control problems and show that the value function is the viscosity solution of the corresponding infinite dimensional Hamilton-Jacobi-Bellman partial differential equation.Mathematics Subject Classification. 49L20, 60H10, 93E20.

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“…We first introduce some notations and definitions which also used in [1,4,5,9]. Let C b be the Banach space of all bounded uniformly continuous functions Φ : C → R with the sup norm…”

Section: The Notions and Definitionsmentioning

confidence: 99%

Section: Notations and Formulation Of The Problemmentioning

confidence: 99%

See 1 more Smart Citation

Dynamic programming principle for stochastic recursive optimal control problem with delayed systems

Chen

2012

ESAIM: COCV

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“…Note that we do not consider state-dependent delays or vanishing lags here. We refer for example to [5,9,12,14,19,20] for a general background on (deterministic and stochastic) functional differential equations (FDEs).…”

Section: H(s X(s)mentioning

confidence: 99%

“…For the term labelled 2) in (20) we first estimate | E (U(t n )|A tn ) | using the definition (19) of U(t n ) and the Lipschitz condition (11) on φ as well as condition (12) on φ i , i = 1, . .…”

Section: Where C < ∞ Is Independent Of H But May Depend On T and On mentioning

confidence: 99%

One-step approximations for stochastic functional differential equations

Buckwar

2006

Applied Numerical Mathematics

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Recursive Stochastic H₂/H_∞ Control Problem for Delay Systems Involving Continuous and Impulse Controls

Qixia

Sun

2016

Asian Journal of Control

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In this paper, we discuss the recursive stochastic H 2 ∕H ∞ control problem of delay systems with random coefficients involving both continuous and impulse controls. By virtue of a new type of forward backward stochastic differential equations, a necessary and sufficient condition for the existence of a unique solution to the control problem under consideration is derived. The existence and uniqueness of the forward backward stochastic differential equations are also be proved.

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Stochastic Differential Systems With Memory: Theory, Examples and Applications

Cited by 132 publications

References 36 publications

Dynamic programming principle for stochastic recursive optimal control problem with delayed systems

Dynamic programming principle for stochastic recursive optimal control problem with delayed systems

One-step approximations for stochastic functional differential equations

Recursive Stochastic H₂/H_∞ Control Problem for Delay Systems Involving Continuous and Impulse Controls

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Stochastic Differential Systems With Memory: Theory, Examples and Applications

Cited by 132 publications

References 36 publications

Dynamic programming principle for stochastic recursive optimal control problem with delayed systems

Dynamic programming principle for stochastic recursive optimal control problem with delayed systems

One-step approximations for stochastic functional differential equations

Recursive Stochastic H2/H∞ Control Problem for Delay Systems Involving Continuous and Impulse Controls

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Product

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Recursive Stochastic H₂/H_∞ Control Problem for Delay Systems Involving Continuous and Impulse Controls