The importance of strictly local martingales; applications to radial Ornstein-Uhlenbeck processes [PDF]
For a wide class of local martingales (M-t) there is a default function, which is not identically zero only when (M-t) is strictly local, i.e. not a true martingale. This 'default' in the martingale property allows us to characterize the integrability of
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Stochastic ODEs and stochastic linear PDEs with critical drift: regularity, duality and uniqueness [PDF]
, 2014 In this paper linear stochastic transport and continuity equations with drift in critical Lp spaces are considered. In this situation noise prevents shocks for the transport equation and singularities in the density for the continuity equation, starting ...
Beck, Lisa +4 more
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Stochastic differential equation modelling of cancer cell migration and tissue invasion. [PDF]
J Math Biol, 2023 Katsaounis D +2 more
europepmc +1 more source
On Markov properties of Lévy waves in two dimensions [PDF]
Markov properties of the solution to the wave equation in two spatial dimensions driven by a Lévy point process are considered. When the velocity of waves is 1, then for domains bounded by a plane, the sharp Markov property is shown to hold if and only ...
Hou, Qiang, Dalang, Robert C.
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Stochastic partial differential equations with Dirichlet white-noise boundary conditions [PDF]
, 2001 . – The paper is devoted to one-dimensional nonlinear stochastic partial differential equations of parabolic type with non homogeneous Dirichlet boundary conditions of white-noise type. We formulate a set of conditions that a random field must satisfy to
Alòs, Elisa +3 more
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Some approximation results for mild solutions of stochastic fractional order evolution equations driven by Gaussian noise. [PDF]
Stoch Partial Differ Equ, 2023 Fahim K, Hausenblas E, Kovács M.
europepmc +1 more source
Moderate Deviations Principle and Central Limit Theorem for Stochastic Cahn-Hilliard Equation in Holder Norm [PDF]
We consider a stochastic Cahn-Hilliard partial differential equation driven by a space-time white noise. In this paper, we prove a Central Limit Theorem (CLT) and a Moderate Deviation Principle (MDP) for a perturbed stochastic Cahn-Hilliard equation in ...
R. M., Ratsarasaina +1 more
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Estimates on moments of the solutions to stochastic differential equations with respect to martingales in the plane [PDF]
Let M = {Mz, z [epsilon] R2+} be a two-parameter strong martingale, A be a two-parameter increasing process on R2+ = [0, + [infinity]) x [0, + [infinity]). Consider the following stochastic differential equations in the plane: for z [epsilon] R2+.
Liang, Zong-xia, Zheng, Ming-li
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Self-averaging from lateral diversity in the ItôSchrödinger equation [PDF]
, 2006 . We consider the random Schrödinger equation as it arises in the paraxial regime for wave propagation in random media. In the white noise limit it becomes the Itô-Schrödinger stochastic partial differential equation (SPDE) which we analyze here in the ...
George Papanicolaou +2 more
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Erratum: Moderate Deviations Principle and Central Limit Theorem for Stochastic Cahn-Hilliard Equation in Hölder Norm [PDF]
We consider a stochastic Cahn-Hilliard partial differential equation driven by a space-time white noise. In this paper, we prove a Central Limit Theorem (CLT) and a Moderate Deviation Principle (MDP) for a perturbed stochastic Cahn-Hilliard equation in ...
R. M., Ratsarasaina +1 more
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