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@prefix dct: <http://purl.org/dc/terms/> .
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    dct:description """
              This PhD thesis studies various mathematical aspects of problems related to the Markovian projection of stochastic processes, and explores some ap- plications of the results obtained to mathematical finance, in the context of semimartingale models. Given a stochastic process ξ, modeled as a semimartingale, our aim is to build a Markov process X whose marginal laws are the same as ξ. This construction allows us to use analytical tools such as integro-differential equa- tions to explore or compute quantities involving the marginal laws of ξ, even when ξ is not Markovian. We present a systematic study of this problem from probabilistic view- point and from the analytical viewpoint. On the probabilistic side, given a discontinuous semimartingale we give an explicit construction of a Markov process X which mimics the marginal distributions of ξ, as the solution of a martingale problems for a certain integro-differential operator. This con- struction extends the approach of Gy ̈ongy to the discontinuous case and applies to a wide range of examples which arise in applications, in particu- lar in mathematical finance. On the analytical side, we show that the flow of marginal distributions of a discontinuous semimartingale is the solution of an integro-differential equation, which extends the Kolmogorov forward equation to a non-Markovian setting. As an application, we derive a forward equation for option prices in a pricing model described by a discontinuous semimartingale. This forward equation generalizes the Dupire equation, orig- inally derived in the case of diffusion models, to the case of a discontinuous semimartingale. These results give an application to the evaluation of index options allowing to reduce the problem of high dimension.
            """ ;
    dct:identifier "tel-00766235" ;
    dct:issued "2026-05-30T14:25:48.759244"^^xsd:dateTime ;
    dct:language "en" ;
    dct:modified "2026-05-30T14:25:48.759253"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "Markovian Projection of Stochastic Processes" ;
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    dcat:keyword "dupire-equation",
        "equation-de-dupire",
        "equation-de-kolmogorov",
        "equation-forward",
        "forward-equation",
        "infoeu-reposemanticsdoctoralthesis",
        "markovian-projection",
        "martingale-problem",
        "mathmath-prmathematics-mathprobability-mathpr",
        "mimicking-theorem",
        "probleme-de-martingale",
        "projection-markovienne",
        "qfinprquantitative-finance-q-finpricing-of-securities-q-finpr",
        "semimartingale",
        "theses" ;
    dcat:landingPage <https://theses.hal.science/tel-00766235> .

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    dct:issued "2026-05-30T14:25:48.915804"^^xsd:dateTime ;
    dct:modified "2026-05-30T14:25:48.703194"^^xsd:dateTime ;
    dct:title "Markovian Projection of Stochastic Processes" ;
    dcat:accessURL <https://theses.hal.science/tel-00766235> .

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