Euler scheme for SDEs with non-Lipschitz diffusion coefficient : strong convergence

Abdel Berkaoui; Mireille Bossy; Awa Diop

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On mean numbers of passage times in small balls of discretized Itô processes.

Bernardin, Frédéric, Bossy, Mireille, Martinez, Miguel, Talay, Denis (2009)

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Dynamical properties and characterization of gradient drift diffusions.

Darses, Sébastian, Nourdin, Ivan (2007)

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Absorption in stochastic epidemics

Josef Štěpán, Jakub Staněk (2009)

Kybernetika

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A two dimensional stochastic differential equation is suggested as a stochastic model for the Kermack–McKendrick epidemics. Its strong (weak) existence and uniqueness and absorption properties are investigated. The examples presented in Section 5 are meant to illustrate possible different asymptotics of a solution to the equation.

Forward-backward stochastic differential equations and PDE with gradient dependent second order coefficients

Romain Abraham, Olivier Riviere (2006)

ESAIM: Probability and Statistics

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We consider a system of fully coupled forward-backward stochastic differential equations. First we generalize the results of Pardoux-Tang [7] concerning the regularity of the solutions with respect to initial conditions. Then, we prove that in some particular cases this system leads to a probabilistic representation of solutions of a second-order PDE whose second order coefficients depend on the gradient of the solution. We then give some examples in dimension 1 and dimension 2 for...