Linear Stochastic Differential Equations Driven by Gauss-Volterra Processes and Related Linear-Quadratic Control Problems

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10402880" target="_blank" >RIV/00216208:11320/19:10402880 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=dQJcMCSDNI" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=dQJcMCSDNI</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00245-017-9468-3" target="_blank" >10.1007/s00245-017-9468-3</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Linear Stochastic Differential Equations Driven by Gauss-Volterra Processes and Related Linear-Quadratic Control Problems

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Linear Stochastic Differential Equations Driven by Gauss-Volterra Processes and Related Linear-Quadratic Control Problems

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10103 - Statistics and probability

Projekt

<a href="/cs/project/GA15-08819S" target="_blank" >GA15-08819S: Stochastické procesy v nekonečně rozměrných prostorech</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Applied Mathematics and Optimization

ISSN

0095-4616

e-ISSN

—

Svazek periodika

80

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

21

Strana od-do

369-389

Kód UT WoS článku

000487033500003

EID výsledku v databázi Scopus

2-s2.0-85038853620