AN L-p-THEORY FOR DIFFUSION EQUATIONS RELATED TO STOCHASTIC PROCESSES WITH NON-STATIONARY INDEPENDENT INCREMENT
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Kim, Ildoo | - |
dc.contributor.author | Kim, Kyeong-Hun | - |
dc.contributor.author | Kim, Panki | - |
dc.date.accessioned | 2021-09-01T17:55:09Z | - |
dc.date.available | 2021-09-01T17:55:09Z | - |
dc.date.created | 2021-06-19 | - |
dc.date.issued | 2019-03-01 | - |
dc.identifier.issn | 0002-9947 | - |
dc.identifier.uri | https://scholar.korea.ac.kr/handle/2021.sw.korea/67044 | - |
dc.description.abstract | Let X = (X-t)(t >= 0) be a stochastic process which has a (not necessarily stationary) independent increment on a probability space (Omega, P). In this paper, we study the following Cauchy problem related to the stochastic process X: (*) partial derivative u/partial derivative t(t,x) = A(t)u(t, x) + f(t, x), u(0, .) = 0, (t,x) is an element of (0, T) x R-d, where f is an element of L-p((0, T);L-p(R-d)) = L-p((0,T);L-p) and A(t)u(t, x) = lim(h down arrow 0) E[u(t, x + Xt+h -X-t) - u(t, x)]/h. We provide a sufficient condition on X (see Assumptions 2.1 and 2.2) to guarantee the unique solvability of equation (*) in L-p([0, T]; H-p(phi)), where H-p(phi) is a phi-potential space on R-d (see Definition 2.9). Furthermore we show that for this solution, parallel to u parallel to L-p ([0, T]; H-p(phi)) (<= N parallel to f parallel to L)(p) ([0, T]; L-p), where N is independent of u and f. | - |
dc.language | English | - |
dc.language.iso | en | - |
dc.publisher | AMER MATHEMATICAL SOC | - |
dc.subject | INTEGRODIFFERENTIAL EQUATIONS | - |
dc.subject | OPERATORS | - |
dc.title | AN L-p-THEORY FOR DIFFUSION EQUATIONS RELATED TO STOCHASTIC PROCESSES WITH NON-STATIONARY INDEPENDENT INCREMENT | - |
dc.type | Article | - |
dc.contributor.affiliatedAuthor | Kim, Ildoo | - |
dc.contributor.affiliatedAuthor | Kim, Kyeong-Hun | - |
dc.identifier.doi | 10.1090/tran/7410 | - |
dc.identifier.scopusid | 2-s2.0-85062006426 | - |
dc.identifier.wosid | 000455249300014 | - |
dc.identifier.bibliographicCitation | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, v.371, no.5, pp.3417 - 3450 | - |
dc.relation.isPartOf | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | - |
dc.citation.title | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | - |
dc.citation.volume | 371 | - |
dc.citation.number | 5 | - |
dc.citation.startPage | 3417 | - |
dc.citation.endPage | 3450 | - |
dc.type.rims | ART | - |
dc.type.docType | Article | - |
dc.description.journalClass | 1 | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.relation.journalResearchArea | Mathematics | - |
dc.relation.journalWebOfScienceCategory | Mathematics | - |
dc.subject.keywordPlus | INTEGRODIFFERENTIAL EQUATIONS | - |
dc.subject.keywordPlus | OPERATORS | - |
dc.subject.keywordAuthor | Diffusion equation for jump process | - |
dc.subject.keywordAuthor | non-stationary increment | - |
dc.subject.keywordAuthor | L-p-theory | - |
dc.subject.keywordAuthor | pseudo-differential operator | - |
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