Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 4 of 4
Full-Text Articles in Entire DC Network
Stochastic Dynamical Systems In Infinite Dimensions, Salah-Eldin A. Mohammed
Stochastic Dynamical Systems In Infinite Dimensions, Salah-Eldin A. Mohammed
Articles and Preprints
We study the local behavior of infinite-dimensional stochastic semiflows near hyperbolic equilibria. The semiflows are generated by stochastic differential systems with finite memory, stochastic evolution equations and semilinear stochastic partial differential equations.
Factoring Families Of Positive Knots On Lorenz-Like Templates, Michael C. Sullivan
Factoring Families Of Positive Knots On Lorenz-Like Templates, Michael C. Sullivan
Articles and Preprints
We show that for m and n positive, composite closed orbits realized on the Lorenz-like template L(m, n) have two prime factors, each a torus knot; and that composite closed orbits on L(−1,−1) have either two for three prime factors, two of which are torus knots.
Hartman-Grobman Theorems Along Hyperbolic Stationary Trajectories, Edson A. Coayla-Teran, Salah-Eldin A. Mohammed, Paulo Régis C. Ruffino
Hartman-Grobman Theorems Along Hyperbolic Stationary Trajectories, Edson A. Coayla-Teran, Salah-Eldin A. Mohammed, Paulo Régis C. Ruffino
Articles and Preprints
We extend the Hartman-Grobman theorems on discrete random dynamical systems (RDS), proved in [7], in two directions: For continuous RDS and for hyperbolic stationary trajectories. In this last case there exists a conjugacy between traveling neighbourhoods of trajectories and neighbourhoods of the origin in the corresponding tangent bundle. We present applications to deterministic dynamical systems.
Discrete-Time Approximations Of Stochastic Delay Equations: The Milstein Scheme, Yaozhong Hu, Salah-Eldin A. Mohammed, Feng Yan
Discrete-Time Approximations Of Stochastic Delay Equations: The Milstein Scheme, Yaozhong Hu, Salah-Eldin A. Mohammed, Feng Yan
Articles and Preprints
In this paper, we develop a strong Milstein approximation scheme for solving stochastic delay differential equations (SDDE's). The scheme has convergence order 1. In order to establish the scheme, we prove an infinite-dimensional Itô formula for "tame" functions acting on the segment process of the solution of an SDDE. It is interesting to note that the presence of the memory in the SDDE requires the use of the Malliavin calculus and the anticipating stochastic analysis of Nualart and Pardoux. Given the non-anticipating nature of the SDDE, the use of anticipating calculus methods appears to be novel.