Matches in SemOpenAlex for { <https://semopenalex.org/work/W4386487679> ?p ?o ?g. }
Showing items 1 to 78 of
78
with 100 items per page.
- W4386487679 endingPage "0" @default.
- W4386487679 startingPage "0" @default.
- W4386487679 abstract "In this paper, we first establish a version of the Feynman-Kac formula for the tempered fractional general diffusion equation $ begin{align} partial^{beta, eta}_{t} u(t,x) = mathfrak{L}u(t,x) +b(t)u(t,x),; ; xinmathcal{X},; tgeq0, end{align} $ with initial value $ f $ belonging to a Banach space $ (mathbb{B}, |cdot|) $, where $ partial^{beta, eta}_{t} $ denotes the Caputo tempered fractional derivative with order $ betain(0,1) $ and tempered parameter $ eta>0 $, $ b(t) $ is a bounded and continuous external potential on $ [0, infty) $, $ mathfrak{L} $ is the infinitesimal generator of a general time-homogeneous strong Markov process $ {X_{t}}_{tgeq0} $, and $ mathcal{X} $ denotes a Lusin space that is a topological space being homeomorphic to a Borel subset of a compact metric space. By using the properties of the tempered $ beta $-stable subordinator $ S_{beta,eta}(t) $ and the inverse tempered $ beta $-stable subordinator $ D_{beta,eta}(t) $, and the stochastic calculus for the stochastic integral driven by $ D_{beta,eta}(t) $, we show that the Feynman-Kac representation $ u(t,x) $ defined by$ begin{align} u(t,x) = {mathbb{E}}^{x}bigg[f(X_{D_{beta,eta}(t)}) e^{int_{0}^{t}b(r)dD_{beta,eta}(r)}bigg] end{align} $is the unique mild and weak solutions to the tempered fractional general diffusion equation. From the Feynman-Kac formula, we further show the continuity of the solution with respect to time based on the integral properties of the Mittag-Leffler function and differential formula of covariance for $ D_{beta,eta}(t) $. By exploring the scaling property of $ D_{beta,eta}(t) $, the explicit order is also presented for the continuity of the solution with respect to tempered parameter $ eta $." @default.
- W4386487679 created "2023-09-07" @default.
- W4386487679 creator A5008641648 @default.
- W4386487679 creator A5085489174 @default.
- W4386487679 date "2023-01-01" @default.
- W4386487679 modified "2023-09-27" @default.
- W4386487679 title "Feynman-Kac formula for tempered fractional general diffusion equations with nonautonomous external potential" @default.
- W4386487679 cites W1495891378 @default.
- W4386487679 cites W1520461790 @default.
- W4386487679 cites W1537749416 @default.
- W4386487679 cites W1966291535 @default.
- W4386487679 cites W1975711585 @default.
- W4386487679 cites W1990932185 @default.
- W4386487679 cites W2038209140 @default.
- W4386487679 cites W2111982684 @default.
- W4386487679 cites W2130025854 @default.
- W4386487679 cites W2131914906 @default.
- W4386487679 cites W2148114839 @default.
- W4386487679 cites W2167580329 @default.
- W4386487679 cites W2266528679 @default.
- W4386487679 cites W2508794727 @default.
- W4386487679 cites W2564031986 @default.
- W4386487679 cites W2898068196 @default.
- W4386487679 cites W2963175785 @default.
- W4386487679 cites W3022439851 @default.
- W4386487679 cites W3025554787 @default.
- W4386487679 cites W3102247295 @default.
- W4386487679 cites W3105065752 @default.
- W4386487679 cites W3207918961 @default.
- W4386487679 cites W4220684525 @default.
- W4386487679 cites W4293200410 @default.
- W4386487679 cites W4295287519 @default.
- W4386487679 doi "https://doi.org/10.3934/dcdsb.2023150" @default.
- W4386487679 hasPublicationYear "2023" @default.
- W4386487679 type Work @default.
- W4386487679 citedByCount "0" @default.
- W4386487679 crossrefType "journal-article" @default.
- W4386487679 hasAuthorship W4386487679A5008641648 @default.
- W4386487679 hasAuthorship W4386487679A5085489174 @default.
- W4386487679 hasBestOaLocation W43864876791 @default.
- W4386487679 hasConcept C105795698 @default.
- W4386487679 hasConcept C112401455 @default.
- W4386487679 hasConcept C114614502 @default.
- W4386487679 hasConcept C134306372 @default.
- W4386487679 hasConcept C2781362121 @default.
- W4386487679 hasConcept C33923547 @default.
- W4386487679 hasConcept C34388435 @default.
- W4386487679 hasConcept C37914503 @default.
- W4386487679 hasConcept C65574998 @default.
- W4386487679 hasConceptScore W4386487679C105795698 @default.
- W4386487679 hasConceptScore W4386487679C112401455 @default.
- W4386487679 hasConceptScore W4386487679C114614502 @default.
- W4386487679 hasConceptScore W4386487679C134306372 @default.
- W4386487679 hasConceptScore W4386487679C2781362121 @default.
- W4386487679 hasConceptScore W4386487679C33923547 @default.
- W4386487679 hasConceptScore W4386487679C34388435 @default.
- W4386487679 hasConceptScore W4386487679C37914503 @default.
- W4386487679 hasConceptScore W4386487679C65574998 @default.
- W4386487679 hasIssue "0" @default.
- W4386487679 hasLocation W43864876791 @default.
- W4386487679 hasOpenAccess W4386487679 @default.
- W4386487679 hasPrimaryLocation W43864876791 @default.
- W4386487679 hasRelatedWork W1598979804 @default.
- W4386487679 hasRelatedWork W1978042415 @default.
- W4386487679 hasRelatedWork W2018828049 @default.
- W4386487679 hasRelatedWork W2042726902 @default.
- W4386487679 hasRelatedWork W2046712581 @default.
- W4386487679 hasRelatedWork W2136053165 @default.
- W4386487679 hasRelatedWork W2159031290 @default.
- W4386487679 hasRelatedWork W2951043270 @default.
- W4386487679 hasRelatedWork W3102909640 @default.
- W4386487679 hasRelatedWork W4298077548 @default.
- W4386487679 hasVolume "0" @default.
- W4386487679 isParatext "false" @default.
- W4386487679 isRetracted "false" @default.
- W4386487679 workType "article" @default.