Abstract
We show how the theory of stochastic flows allows to recover in an elementary way a well known result of Warren on the sticky Brownian motion equation.
Highlights
A θ-sticky Brownian on the half line [0, ∞) is a diffusion with generator (Af )(x) = 1 2 f ′′(x) θf ′(0+)if x > 0 if x = 0 and domainD(A) = f ∈ C2(0, ∞) : f ∈ C0([0, ∞)), f ′(0+), f ′′(0+) exist, f ′′(0+) = 2θf ′(0+), lim f ′′(x) = 0 x→∞where θ > 0 is the stickiness parameter
We show how the theory of stochastic flows allows to recover in an elementary way a well known result of Warren on the sticky Brownian motion equation
Where θ > 0 is the stickiness parameter. This is a special case of Feller one dimensional diffusions introduced by Feller by means of their infinitesimal generators [4]
Summary
To cite this version: Hatem Hajri, Caglar Mine, Marc Arnaudon. APPLICATION OF STOCHASTIC FLOWS TO THE STICKY BROWNIAN MOTION EQUATION. Electronic Communications in Probability, Institute of Mathematical Statistics (IMS), 2016. L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés
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