Markovian Projection of Stochastic Processes
type: Dataset
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.
landing page: https://theses.hal.science/tel-00766235
keyword: dupire-equation
keyword: equation-de-dupire
keyword: equation-de-kolmogorov
keyword: equation-forward
keyword: forward-equation
keyword: infoeu-reposemanticsdoctoralthesis
keyword: markovian-projection
keyword: martingale-problem
keyword: mathmath-prmathematics-mathprobability-mathpr
keyword: mimicking-theorem
keyword: probleme-de-martingale
keyword: projection-markovienne
keyword: qfinprquantitative-finance-q-finpricing-of-securities-q-finpr
keyword: semimartingale
keyword: theses
issued: 2026-05-30T14:25:48.759244
modified: 2026-05-30T14:25:48.759253
language: en
contact point: Organization
  fn: CCSD

test_moissonnage_selune
type: Agent

Markovian Projection of Stochastic Processes
type: Distribution
format: HTML
access URL: https://theses.hal.science/tel-00766235
issued: 2026-05-30T14:25:48.915804
modified: 2026-05-30T14:25:48.703194