Matches in SemOpenAlex for { <https://semopenalex.org/work/W4287201714> ?p ?o ?g. }
- W4287201714 endingPage "1091" @default.
- W4287201714 startingPage "1029" @default.
- W4287201714 abstract "Motivated by entropic optimal transport, we are interested in the Feynman-Kac formula associated to the parabolic equation $$ ( {mathsf {L}}+V)g =0$$ with a final nonnegative boundary condition and a Markov generator $$ {mathsf {L}}:= partial _t + {mathsf {b}}!cdot !nabla + Delta _{ {mathsf {a}}}/2$$ . It is well-known that when the drift $$ {mathsf {b}}$$ , the diffusion matrix $$ {mathsf {a}}$$ and the scalar potential V are regular enough and not growing too fast, the classical solution g of this PDE, is represented by the Feynman-Kac formula $$ g_t(x)=E_R[exp left( int _{[t,T]} V(s,X_s),dsright) g(X_T)mid X_t=x] $$ where R is the Markov measure with generator $$ {mathsf {L}}$$ . We do not assume that g, $$ {mathsf {b}}$$ and V are regular, and only require that their growth is controlled by a finite entropy condition. These hypotheses are less restrictive than the standard assumptions of the theory of viscosity solutions, and allow for instance V to belong to some Kato class. We prove that g defined by the Feynman-Kac formula belongs to the domain of the extended generator $$ {mathcal {L}}$$ of the Markov measure R and satisfies the trajectorial identity: $$ [({mathcal {L}} +V)g] (t,X_t)=0, dtdPtext {-}{a.e.}$$ where the path measure P is defined by $$ P:= f(X_0)exp left( int _{[0,T]}V(t,X_t),dtright) g(X_T) R, $$ with $$ f:{mathbb {R}}^nrightarrow [0, infty )$$ another nonnegative function. We also show that the forward drift $$ {mathsf {b}}^P$$ of P satisfies $$ {mathsf {b}}^P(t,X_t)=[ {mathsf {b}}+ {mathsf {a}}{widetilde{nabla }}log g](t,X_t),$$ $$dtdPtext {-}{a.e.},$$ where $${widetilde{nabla }}$$ is some extension of the standard derivative. Our probabilistic approach relies on stochastic derivatives, semimartingales, Girsanov’s theorem and the Hamilton-Jacobi-Bellman equation satisfied by $$log g$$ ." @default.
- W4287201714 created "2022-07-25" @default.
- W4287201714 creator A5045771047 @default.
- W4287201714 date "2022-08-05" @default.
- W4287201714 modified "2023-10-13" @default.
- W4287201714 title "Feynman-Kac formula under a finite entropy condition" @default.
- W4287201714 cites W140231913 @default.
- W4287201714 cites W1545063325 @default.
- W4287201714 cites W1545370368 @default.
- W4287201714 cites W1549206114 @default.
- W4287201714 cites W1555314858 @default.
- W4287201714 cites W1577627982 @default.
- W4287201714 cites W1651825204 @default.
- W4287201714 cites W1699375872 @default.
- W4287201714 cites W175559256 @default.
- W4287201714 cites W189191968 @default.
- W4287201714 cites W1970457327 @default.
- W4287201714 cites W1975711585 @default.
- W4287201714 cites W1997093580 @default.
- W4287201714 cites W1998107368 @default.
- W4287201714 cites W2012244785 @default.
- W4287201714 cites W2062317971 @default.
- W4287201714 cites W2077493276 @default.
- W4287201714 cites W2128669232 @default.
- W4287201714 cites W2135044418 @default.
- W4287201714 cites W2143083943 @default.
- W4287201714 cites W2143588546 @default.
- W4287201714 cites W2963170010 @default.
- W4287201714 cites W2963345940 @default.
- W4287201714 cites W2963725315 @default.
- W4287201714 cites W40113038 @default.
- W4287201714 cites W4205305373 @default.
- W4287201714 cites W4246156563 @default.
- W4287201714 cites W4249821837 @default.
- W4287201714 cites W4299832460 @default.
- W4287201714 cites W4300023393 @default.
- W4287201714 cites W4301074654 @default.
- W4287201714 cites W45882642 @default.
- W4287201714 cites W631502879 @default.
- W4287201714 cites W642874938 @default.
- W4287201714 doi "https://doi.org/10.1007/s00440-022-01155-8" @default.
- W4287201714 hasPublicationYear "2022" @default.
- W4287201714 type Work @default.
- W4287201714 citedByCount "0" @default.
- W4287201714 crossrefType "journal-article" @default.
- W4287201714 hasAuthorship W4287201714A5045771047 @default.
- W4287201714 hasBestOaLocation W42872017142 @default.
- W4287201714 hasConcept C114614502 @default.
- W4287201714 hasConcept C121332964 @default.
- W4287201714 hasConcept C163258240 @default.
- W4287201714 hasConcept C2524010 @default.
- W4287201714 hasConcept C2779557605 @default.
- W4287201714 hasConcept C2780009758 @default.
- W4287201714 hasConcept C2780992000 @default.
- W4287201714 hasConcept C33923547 @default.
- W4287201714 hasConcept C37914503 @default.
- W4287201714 hasConcept C41008148 @default.
- W4287201714 hasConcept C54207081 @default.
- W4287201714 hasConcept C57691317 @default.
- W4287201714 hasConcept C62520636 @default.
- W4287201714 hasConcept C65574998 @default.
- W4287201714 hasConcept C77088390 @default.
- W4287201714 hasConceptScore W4287201714C114614502 @default.
- W4287201714 hasConceptScore W4287201714C121332964 @default.
- W4287201714 hasConceptScore W4287201714C163258240 @default.
- W4287201714 hasConceptScore W4287201714C2524010 @default.
- W4287201714 hasConceptScore W4287201714C2779557605 @default.
- W4287201714 hasConceptScore W4287201714C2780009758 @default.
- W4287201714 hasConceptScore W4287201714C2780992000 @default.
- W4287201714 hasConceptScore W4287201714C33923547 @default.
- W4287201714 hasConceptScore W4287201714C37914503 @default.
- W4287201714 hasConceptScore W4287201714C41008148 @default.
- W4287201714 hasConceptScore W4287201714C54207081 @default.
- W4287201714 hasConceptScore W4287201714C57691317 @default.
- W4287201714 hasConceptScore W4287201714C62520636 @default.
- W4287201714 hasConceptScore W4287201714C65574998 @default.
- W4287201714 hasConceptScore W4287201714C77088390 @default.
- W4287201714 hasIssue "3-4" @default.
- W4287201714 hasLocation W42872017141 @default.
- W4287201714 hasLocation W42872017142 @default.
- W4287201714 hasLocation W42872017143 @default.
- W4287201714 hasLocation W42872017144 @default.
- W4287201714 hasLocation W42872017145 @default.
- W4287201714 hasLocation W42872017146 @default.
- W4287201714 hasLocation W42872017147 @default.
- W4287201714 hasLocation W42872017148 @default.
- W4287201714 hasLocation W42872017149 @default.
- W4287201714 hasOpenAccess W4287201714 @default.
- W4287201714 hasPrimaryLocation W42872017141 @default.
- W4287201714 hasRelatedWork W1539596337 @default.
- W4287201714 hasRelatedWork W1855007440 @default.
- W4287201714 hasRelatedWork W2116736487 @default.
- W4287201714 hasRelatedWork W2156911440 @default.
- W4287201714 hasRelatedWork W2229925025 @default.
- W4287201714 hasRelatedWork W2557979085 @default.
- W4287201714 hasRelatedWork W2788247819 @default.
- W4287201714 hasRelatedWork W33469805 @default.
- W4287201714 hasRelatedWork W4238831369 @default.