Ergodicity for locally monotone stochastic evolution equations with L\'evy noise
We establish general conditions for stochastic evolution equations with locally monotone drift and degenerate additive L\'evy noise in variational formulation resulting in the existence of a unique invariant probability measure for the associated ergodic Markovian Feller semigroup. We prove imp...
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| creator | Barrera, Gerardo Tölle, Jonas M |
| description | We establish general conditions for stochastic evolution equations with
locally monotone drift and degenerate additive L\'evy noise in variational
formulation resulting in the existence of a unique invariant probability
measure for the associated ergodic Markovian Feller semigroup. We prove
improved moment estimates for the solutions and the $e$-property of the
semigroup. Examples include the stochastic incompressible 2D Navier-Stokes
equations, shear thickening stochastic power-law fluid equations, the
stochastic heat equation, as well as, stochastic semilinear equations such as
the 1D stochastic Burgers equation. |
| doi_str_mv | 10.48550/arxiv.2412.01381 |
| format | Article |
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locally monotone drift and degenerate additive L\'evy noise in variational
formulation resulting in the existence of a unique invariant probability
measure for the associated ergodic Markovian Feller semigroup. We prove
improved moment estimates for the solutions and the $e$-property of the
semigroup. Examples include the stochastic incompressible 2D Navier-Stokes
equations, shear thickening stochastic power-law fluid equations, the
stochastic heat equation, as well as, stochastic semilinear equations such as
the 1D stochastic Burgers equation.</description><identifier>DOI: 10.48550/arxiv.2412.01381</identifier><language>eng</language><subject>Mathematics - Analysis of PDEs ; Mathematics - Dynamical Systems ; Mathematics - Functional Analysis ; Mathematics - Probability</subject><creationdate>2024-12</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2412.01381$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2412.01381$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Barrera, Gerardo</creatorcontrib><creatorcontrib>Tölle, Jonas M</creatorcontrib><title>Ergodicity for locally monotone stochastic evolution equations with L\'evy noise</title><description>We establish general conditions for stochastic evolution equations with
locally monotone drift and degenerate additive L\'evy noise in variational
formulation resulting in the existence of a unique invariant probability
measure for the associated ergodic Markovian Feller semigroup. We prove
improved moment estimates for the solutions and the $e$-property of the
semigroup. Examples include the stochastic incompressible 2D Navier-Stokes
equations, shear thickening stochastic power-law fluid equations, the
stochastic heat equation, as well as, stochastic semilinear equations such as
the 1D stochastic Burgers equation.</description><subject>Mathematics - Analysis of PDEs</subject><subject>Mathematics - Dynamical Systems</subject><subject>Mathematics - Functional Analysis</subject><subject>Mathematics - Probability</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNqFjr0KwjAURrM4iPoATt7Nydr0B7pLxcHBwVEoIab2QpqrSRrN20uLu9P5hgPfYWzN06SoyjLdC_vBkGQFz5KU5xWfs0ttH3RHiT5CSxY0SaF1hJ4MeTIKnCfZCedRggqkB49kQL0GMQ4Hb_QdnG9bFSIYQqeWbNYK7dTqxwXbHOvr4bSbvpunxV7Y2IwNzdSQ_ze-g6M9jw</recordid><startdate>20241202</startdate><enddate>20241202</enddate><creator>Barrera, Gerardo</creator><creator>Tölle, Jonas M</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20241202</creationdate><title>Ergodicity for locally monotone stochastic evolution equations with L\'evy noise</title><author>Barrera, Gerardo ; Tölle, Jonas M</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-arxiv_primary_2412_013813</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Mathematics - Analysis of PDEs</topic><topic>Mathematics - Dynamical Systems</topic><topic>Mathematics - Functional Analysis</topic><topic>Mathematics - Probability</topic><toplevel>online_resources</toplevel><creatorcontrib>Barrera, Gerardo</creatorcontrib><creatorcontrib>Tölle, Jonas M</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Barrera, Gerardo</au><au>Tölle, Jonas M</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Ergodicity for locally monotone stochastic evolution equations with L\'evy noise</atitle><date>2024-12-02</date><risdate>2024</risdate><abstract>We establish general conditions for stochastic evolution equations with
locally monotone drift and degenerate additive L\'evy noise in variational
formulation resulting in the existence of a unique invariant probability
measure for the associated ergodic Markovian Feller semigroup. We prove
improved moment estimates for the solutions and the $e$-property of the
semigroup. Examples include the stochastic incompressible 2D Navier-Stokes
equations, shear thickening stochastic power-law fluid equations, the
stochastic heat equation, as well as, stochastic semilinear equations such as
the 1D stochastic Burgers equation.</abstract><doi>10.48550/arxiv.2412.01381</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Analysis of PDEs Mathematics - Dynamical Systems Mathematics - Functional Analysis Mathematics - Probability |
| title | Ergodicity for locally monotone stochastic evolution equations with L\'evy noise |
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