On the unique solvability of some nonlinear stochastic PDEs.
Yoo, Hyek (1998)
Electronic Journal of Probability [electronic only]
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Displaying similar documents to “Linear stochastic parabolic equations, degenerating on the boundary of a domain.”
On the unique solvability of some nonlinear stochastic PDEs.
Support of a Marcus equation in dimension 1.
Simon, Thomas (2000)
Electronic Communications in Probability [electronic only]
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Quasiderivatives and interior smoothness of harmonic functions associated with degenerate diffusion processes.
Krylov, N.V. (2004)
Electronic Journal of Probability [electronic only]
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SPDEs in spaces.
Krylov, N.V. (2000)
Electronic Journal of Probability [electronic only]
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On the discretization in time of parabolic stochastic partial differential equations
Jacques Printems (2001)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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We first generalize, in an abstract framework, results on the order of convergence of a semi-discretization in time by an implicit Euler scheme of a stochastic parabolic equation. In this part, all the coefficients are globally Lipchitz. The case when the nonlinearity is only locally Lipchitz is then treated. For the sake of simplicity, we restrict our attention to the Burgers equation. We are not able in this case to compute a pathwise order of the approximation, we introduce the weaker...
Variational analysis for the Black and Scholes equation with stochastic volatility
Yves Achdou, Nicoletta Tchou (2002)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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We propose a variational analysis for a Black and Scholes equation with stochastic volatility. This equation gives the price of a European option as a function of the time, of the price of the underlying asset and of the volatility when the volatility is a function of a mean reverting Orstein-Uhlenbeck process, possibly correlated with the underlying asset. The variational analysis involves weighted Sobolev spaces. It enables to prove qualitative properties of the solution, namely a...
A converse comparison theorem for BSDEs and related properties of -expectation.
Briand, Philippe, Coquet, François, Hu, Ying, Mémin, Jean, Peng, Shige (2000)
Electronic Communications in Probability [electronic only]
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An extended generator and Schrödinger equations.
Getoor, R.K. (1999)
Electronic Journal of Probability [electronic only]
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Intrinsic location parameter of a diffusion process.
Darling, R.W.R. (2002)
Electronic Journal of Probability [electronic only]
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On a nonlocal singular mixed evolution problem.
Mesloub, Said, Lekrine, Nadia (2001)
Matematichki Vesnik
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A note on Krylov's -theory for systems of SPDEs.
Mikulevicius, R., Rozovskii, B. (2001)
Electronic Journal of Probability [electronic only]
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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...