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Full-Text Articles in Mathematics
Stochastic Functional Differential Equations On Manifolds (Conference On Probability And Geometry), Salah-Eldin A. Mohammed
Stochastic Functional Differential Equations On Manifolds (Conference On Probability And Geometry), Salah-Eldin A. Mohammed
Miscellaneous (presentations, translations, interviews, etc)
We prove an existence theorem for solutions of stochastic functional differential equations under smooth constraints in Euclidean space. The initial states are semimartingales on a compact Riemannian manifold. It is shown that, under suitable regularity hypotheses on the coefficients, and given an initial semimartingale, a sfde on a compact manifold admits a unique solution living on the manifold for all time. We also discuss the Chen-Souriau regularity of the solution of the sfde in the initial process. The results are joint work with Remi Leandre.
The Stable Manifold Theorem For Stochastic Systems With Memory (Probability Seminar, Université Henri Poincaré Nancy 1), Salah-Eldin A. Mohammed
The Stable Manifold Theorem For Stochastic Systems With Memory (Probability Seminar, Université Henri Poincaré Nancy 1), Salah-Eldin A. Mohammed
Miscellaneous (presentations, translations, interviews, etc)
We state and prove a Local Stable Manifold Theorem for nonlinear stochastic differential systems with finite memory (viz. stochastic functional differential equations (sfde's)). We introduce the notion of hyperbolicity for stationary solutions of sfde's. We then establish the existence of smooth stable and unstable manifolds in a neighborhood of a hyperbolic stationary solution. The stable and unstable manifolds are stationary and asymptotically invariant under the stochastic semiflow. The proof uses infinite-dimensional multiplicative ergodic theory techniques and interpolation arguments.
Small Extensions Of Witt Rings, Robert W. Fitzgerald
Small Extensions Of Witt Rings, Robert W. Fitzgerald
Articles and Preprints
We consider certain Witt ring extensions S of a noetherian Witt ring R obtained by adding one new generator. The conditions on the new generator are those known to hold when R is the Witt ring of a Field F, S is the Witt ring of a Field K and K/F is an odd degree extension. We show that if R is of elementary type then so is S.
Single-Change Circular Covering Designs, John P. Mcsorley
Single-Change Circular Covering Designs, John P. Mcsorley
Articles and Preprints
A single-change circular covering design (scccd) based on the set [v] = {1, . . . ,v} with block size k is an ordered collection of b blocks, B = {B1, . . . ,Bb}, each Bi ⊂ [v], which obey: (1) each block differs from the previous block by a single element, as does the last from the first, and, (2) every pair of [v] is covered by some Bi. The object is to minimize b for a fixed v and k. …
The Stable Manifold Theorem For Stochastic Differential Equations, Salah-Eldin A. Mohammed, Michael K. R. Scheutzow
The Stable Manifold Theorem For Stochastic Differential Equations, Salah-Eldin A. Mohammed, Michael K. R. Scheutzow
Articles and Preprints
We formulate and prove a local stable manifold theorem for stochastic differential equations (SDEs) that are driven by spatial Kunita-type semimartingales with stationary ergodic increments. Both Stratonovich and Itô-type equations are treated. Starting with the existence of a stochastic flow for a SDE, we introduce the notion of a hyperbolic stationary trajectory. We prove the existence of invariant random stable and unstable manifolds in the neighborhood of the hyperbolic stationary solution. For Stratonovich SDEs, the stable and unstable manifolds are dynamically characterized using forward and backward solutions of the anticipating SDE. The proof of the stable manifold theorem is based …