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                <title xml:lang="en">Stochastic Analysis of non-Markovian irregular phenomena</title>
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                <authority type="supervisor">Francesco Russo</authority>
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                <term xml:lang="en">Backward stochastic differential equations</term>
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                <term xml:lang="en">Stochastic calculus via regularization</term>
                <term xml:lang="en">Irregular phenomena</term>
                <term xml:lang="fr">Chemin rugueux</term>
                <term xml:lang="fr">Equations différentielles stochastiques rétrogrades</term>
                <term xml:lang="fr">Calcul stochastique via régularisation</term>
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              <p>This thesis focuses on some particular stochastic analysis aspects of non-Markovian irregular phenomena. It formulates existence and uniqueness for some martingale problems involving two types of irregulat drifts perturbed by path-dependant functionals: the first one is related to the case which is the derivative of continuous function and it models irregular path-dependent media; the second one concerns the case when the drift is of Bessel type in low dimension. Finally the thesis also focuses on rough paths techniques and its relation with the stochastic calculus via regularization.</p>
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              <p>Cette thèse se concentre sur certains aspects d'analyse stochastique de modèles non-markoviens irréguliers. On formule existence et unicité pour certains problèmes de martingales impliquant deux types de dérive irrégulière perturbée par des fonctionnelles dépendant de la trajectoire. Dans le premier cas, on considère le cas où la dérive est la dérivée d'une fonction continue: le modèle correspondant est celui de milieux aléatoires irréguliers dépendant de la trajectoire. Le second concerne le cas où la dérive est celui d'un processus de Bessel en basse dimension: dans ce cas il est bien connu qu'en général les processus ne sont pas des semimartingales. Enfin la thèse explore également des relations et des analogies entre la théorie des chemins rugueux et le calcul stochastique via régularisation.</p>
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