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The existence and exponential behavior of solutions to stochastic delay evolution equations with a fractional Brownian motion
In this paper we investigate the existence, uniqueness and exponential asymptotic behavior of mild solutions to stochastic delay evolution equations perturbed by a fractional Brownian motion B Q H ( t ) : d X ( t ) = ( A X ( t ) + f ( t , X t ) ) d t + g ( t ) d B Q H ( t ) , with Hurst parameter H...
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| Published in: | Nonlinear analysis 2011-07, Vol.74 (11), p.3671-3684 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c398t-71bf2987c4a296415482388a4c25933b1396a3f2db52823c92f9aec9ca8550e43 |
| container_end_page | 3684 |
| container_issue | 11 |
| container_start_page | 3671 |
| container_title | Nonlinear analysis |
| container_volume | 74 |
| creator | Caraballo, T. Garrido-Atienza, M.J. Taniguchi, T. |
| description | In this paper we investigate the existence, uniqueness and exponential asymptotic behavior of mild solutions to stochastic delay evolution equations perturbed by a fractional Brownian motion
B
Q
H
(
t
)
:
d
X
(
t
)
=
(
A
X
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t
)
+
f
(
t
,
X
t
)
)
d
t
+
g
(
t
)
d
B
Q
H
(
t
)
,
with Hurst parameter
H
∈
(
1
/
2
,
1
)
. We also consider the existence of weak solutions. |
| doi_str_mv | 10.1016/j.na.2011.02.047 |
| format | article |
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(
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with Hurst parameter
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H
(
t
)
:
d
X
(
t
)
=
(
A
X
(
t
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(
t
,
X
t
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)
d
t
+
g
(
t
)
d
B
Q
H
(
t
)
,
with Hurst parameter
H
∈
(
1
/
2
,
1
)
. We also consider the existence of weak solutions.</description><subject>Asymptotic properties</subject><subject>Brownian motion</subject><subject>Delay</subject><subject>Delay stochastic PDEs</subject><subject>Evolution</subject><subject>Exact sciences and technology</subject><subject>Exponential decay in mean square</subject><subject>Fractional Brownian motion</subject><subject>Global analysis, analysis on manifolds</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Partial differential equations</subject><subject>Sciences and techniques of general use</subject><subject>Stochasticity</subject><subject>Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</subject><subject>Uniqueness</subject><issn>0362-546X</issn><issn>1873-5215</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><recordid>eNp1kL1vFDEQxS0EEkegp3SDqHbjj_WuTQdRSJAi0SRSOmvOO6vzac--2L4LKfjf8epOdKlGM-83bzSPkM-ctZzx_nLbBmgF47xlomXd8IasuB5kowRXb8mKyV40qusf35MPOW8ZY3yQ_Yr8vd8gxT8-FwwOKYSxdvsYMBQPM13jBo4-JhonmuN8KD6GTEukuUS3gVy8oyPO8ELxeJYpPh3gxD37sqFApwRuGVS_Hyk-Bw-B7uIy-UjeTTBn_HSuF-Th5_X91W1z9_vm19X3u8ZJo0sz8PUkjB5cB8L0HVedFlJr6JxQRso1l6YHOYlxrURVnBGTAXTGgVaKYScvyNeT7z7FpwPmYnc-O5xnCBgP2WrN-l4wJSrJTqRLMeeEk90nv4P0YjmzS9B2awPYJWjLhK1B15UvZ3PIDub6bXA-_98THTeMaV65bycO66dHj8lm55fUR5_QFTtG__qRf7RRlFI</recordid><startdate>20110701</startdate><enddate>20110701</enddate><creator>Caraballo, T.</creator><creator>Garrido-Atienza, M.J.</creator><creator>Taniguchi, T.</creator><general>Elsevier Ltd</general><general>Elsevier</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20110701</creationdate><title>The existence and exponential behavior of solutions to stochastic delay evolution equations with a fractional Brownian motion</title><author>Caraballo, T. ; Garrido-Atienza, M.J. ; Taniguchi, T.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c398t-71bf2987c4a296415482388a4c25933b1396a3f2db52823c92f9aec9ca8550e43</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Asymptotic properties</topic><topic>Brownian motion</topic><topic>Delay</topic><topic>Delay stochastic PDEs</topic><topic>Evolution</topic><topic>Exact sciences and technology</topic><topic>Exponential decay in mean square</topic><topic>Fractional Brownian motion</topic><topic>Global analysis, analysis on manifolds</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Partial differential equations</topic><topic>Sciences and techniques of general use</topic><topic>Stochasticity</topic><topic>Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</topic><topic>Uniqueness</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Caraballo, T.</creatorcontrib><creatorcontrib>Garrido-Atienza, M.J.</creatorcontrib><creatorcontrib>Taniguchi, T.</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Nonlinear analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Caraballo, T.</au><au>Garrido-Atienza, M.J.</au><au>Taniguchi, T.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The existence and exponential behavior of solutions to stochastic delay evolution equations with a fractional Brownian motion</atitle><jtitle>Nonlinear analysis</jtitle><date>2011-07-01</date><risdate>2011</risdate><volume>74</volume><issue>11</issue><spage>3671</spage><epage>3684</epage><pages>3671-3684</pages><issn>0362-546X</issn><eissn>1873-5215</eissn><coden>NOANDD</coden><abstract>In this paper we investigate the existence, uniqueness and exponential asymptotic behavior of mild solutions to stochastic delay evolution equations perturbed by a fractional Brownian motion
B
Q
H
(
t
)
:
d
X
(
t
)
=
(
A
X
(
t
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+
f
(
t
,
X
t
)
)
d
t
+
g
(
t
)
d
B
Q
H
(
t
)
,
with Hurst parameter
H
∈
(
1
/
2
,
1
)
. We also consider the existence of weak solutions.</abstract><cop>Amsterdam</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.na.2011.02.047</doi><tpages>14</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0362-546X |
| ispartof | Nonlinear analysis, 2011-07, Vol.74 (11), p.3671-3684 |
| issn | 0362-546X 1873-5215 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_880662052 |
| source | Elsevier SD Backfile Mathematics; Elsevier |
| subjects | Asymptotic properties Brownian motion Delay Delay stochastic PDEs Evolution Exact sciences and technology Exponential decay in mean square Fractional Brownian motion Global analysis, analysis on manifolds Mathematical analysis Mathematics Partial differential equations Sciences and techniques of general use Stochasticity Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds Uniqueness |
| title | The existence and exponential behavior of solutions to stochastic delay evolution equations with a fractional Brownian motion |
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