Linear Stochastic Differential Equations Driven by Gauss-Volterra Processes and Related Linear-Quadratic Control Problems
Result description
A stochastic linear-quadratic control problem is formulated and solved for some stochastic equations in an infinite dimensional Hilbert space for both finite and infinite time horizons. The equations are bilinear in the state and the noise process where the noise is a scalar Gauss-Volterra process. TheGauss-Volterra noise processes are obtained from the integral of a Brownian motion with a suitable kernel function. These noise processes include fractional Brownian motions with the Hurst parameter H is an element of (1/2, 1), Liouville fractional Brownian motions with H is an element of (1/2, 1), and some multifractional Brownian motions. The family of admissible controls for the quadratic costs is a family of linear feedback controls. This restriction on the family of controls allows for a feasible implementation of the optimal controls. The bilinear equations have drift terms that are linear evolution operators. These equations can model stochastic partial differential equations of parabolic and hyperbolic types and two families of examples are given.
Keywords
Linear-Quadratic Control ProblemsGauss-Volterra ProcessesLinear Stochastic Differential Equations
The result's identifiers
Result code in IS VaVaI
Result on the web
https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=dQJcMCSDNI
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
Linear Stochastic Differential Equations Driven by Gauss-Volterra Processes and Related Linear-Quadratic Control Problems
Original language description
A stochastic linear-quadratic control problem is formulated and solved for some stochastic equations in an infinite dimensional Hilbert space for both finite and infinite time horizons. The equations are bilinear in the state and the noise process where the noise is a scalar Gauss-Volterra process. TheGauss-Volterra noise processes are obtained from the integral of a Brownian motion with a suitable kernel function. These noise processes include fractional Brownian motions with the Hurst parameter H is an element of (1/2, 1), Liouville fractional Brownian motions with H is an element of (1/2, 1), and some multifractional Brownian motions. The family of admissible controls for the quadratic costs is a family of linear feedback controls. This restriction on the family of controls allows for a feasible implementation of the optimal controls. The bilinear equations have drift terms that are linear evolution operators. These equations can model stochastic partial differential equations of parabolic and hyperbolic types and two families of examples are given.
Czech name
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Czech description
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Classification
Type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10103 - Statistics and probability
Result continuities
Project
GA15-08819S: Stochastic Processes in Infinite Dimensional Spaces
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Applied Mathematics and Optimization
ISSN
0095-4616
e-ISSN
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Volume of the periodical
80
Issue of the periodical within the volume
2
Country of publishing house
DE - GERMANY
Number of pages
21
Pages from-to
369-389
UT code for WoS article
000487033500003
EID of the result in the Scopus database
2-s2.0-85038853620
Basic information
Result type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
OECD FORD
Statistics and probability
Year of implementation
2019