Books and Articles

-Salah Mohammed

Research Monographs:

Retarded Functional Differential Equations: A Global Point of View, Research Notes in Mathematics No. 21, Pitman Publishing Ltd., London-San Francisco-Melbourne (1978), pp. 147.
Stochastic Functional Differential Equations, Research Notes in Mathematics No. 99, Pitman Books Ltd., London (1984), pp. 245.
Stochastic Differential Systems with Memory, (In preparation), click below to view the Introduction and the List of Contents:

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Articles:

``Separation of Variables: An Abstract Approach", Proceedings of the Royal Society of Edinburgh (A), 72, 5, (1972--1973), 57-78.
``Markov Solutions of Stochastic Functional Differential Equations", Proceedings of the Second International Conference on Functional Differential Systems and Related Topics (May 1981), Ed. M. Kisielewicz, Polish Academy of Sciences (1981).
``The Infinitesimal Generator of a Stochastic Functional Differential Equation", Springer Lecture Notes in Mathematics, 964, Springer--Verlag, Berlin-Heidelberg-New York (1982), 529-538
``Almost Surely Non-linear Solutions of Stochastic Linear Delay Equations", Springer Lecture Notes in Mathematics 1151, Springer-Verlag (1985), pp. 270-275.
``Stability of Linear Delay Equations under a Small Noise," Proceedings of the Edinburgh Mathematical Society, 29, (1986), 233-254 .
``Hyperbolic State Space Decomposition for a Linear Stochastic Delay Equation" (with M. Scheutzow and H.V. Weizsacker), SIAM Journal on Control and Optimization 24-3, (1986), 543-551 .
``Non-Linear Flows for Linear Stochastic Delay Equations," Stochastics Vol. l7 #3, (1987), 207-212
``Unstable Invariant Distributions for a Class of Stochastic Delay Equations," Proceedings of Edinburgh Mathematical Society, 31, (1988), 1-23
``On the Solution of Stochastic Ordinary Differential Equations via Small Delays" (with D. R. Bell), Stochastics Vol. 28, No. 4, (1989), 293-299 .
``Lyapunov Exponents and Stationary Solutions for Affine Stochastic Delay Equations" (with M. Scheutzow), Stochastics and Stochastic Reports, Vol. 29, No. 2 (1990), 259-283.
``The Lyapunov Spectrum and Stable Manifolds for Stochastic Linear Delay Equations," I.M.A. Series #323, pp. 57, Stochastics and Stochastic Reports, Vol. 29 (1990), 89-131.
``The Malliavin Calculus and Stochastic Delay Equations," (with D.R. Bell), Journal of Functional Analysis, Vol. 99, No. 1 (1991), 75-99.
``Lyapunov Exponents and Stochastic Flows of Linear and Affine Hereditary Systems," Diffusion Processes and Related Problems in Analysis, Vol. II, edited by Mark Pinsky and Volker Wihstutz, Birkhauser (1992), 141-169.
``Op&eacuterateurs Paraboliques Hypoelliptiques Avec D&eacuteg&eacuten&eacuterescences Exponentielles," (with Denis Bell) C.R. Acad. Sci. Paris (French Academy of Sciences), t. 317, S'erie I, (1993), 1059--1064 .
``Degenerate Stochastic Differential Equations, Flows and Hypoellipticity," (with Denis Bell) (Invited Paper), AMS Summer Research Institute on Stochastic Analysis, Ithaca, Cornell 1993, Proceedings of Symposia in Pure Mathematics, American Mathematical Society, Vol. 57, Stochastic Analysis, American Mathematical Society, Providence, Rhode Island (1995), 553-564.
``Smooth Densities for Degenerate Stochastic Delay Equations with Hereditary Drift" (with Denis Bell), The Annals of Probability, Vol. 23, No. 4, (1995), 1875-1894.
``An Extension of H&oumlrmander's Theorem for Infinitely Degenerate Second-Order Operators," (with Denis Bell), Duke Mathematical Journal , Vol.78, No. 3, (1995), 453-475.
``Lyapunov Exponents of Linear and Stochastic Functional Differential Equations Driven by Semimartingales, Part I: The Multiplicative Ergodic Theory (with M. Scheutzow), Annals of Institute of Henri Poincaré, Probabilites &eacutet Statistiques Vol. 32, 1, (1996), 69-105.
``Lyapunov Exponents of Linear Stochastic Functional Differential Equations, Part II: Examples and Case Studies" (With M. Scheutzow), The Annals of Probability, Vol. 25, No. 3, (1997), 1210-1240.
``Spatial Estimates for Stochastic Flows in Euclidean Space" (With M. Scheutzow), The Annals of Probability, Vol. 26, No. 1, (1998), 56-77.
``Stochastic Differential Systems with Memory: Theory, Examples and Applications", Stochastic Analysis and Related Topics VI. The Geilo Workshop, 1996 , ed. L. Decreusefond, Jon Gjerde, B. Oksendal, A.S. Ustunel, Progress in Probability, Birkhauser (1998), 1-77. (Invited presentation of six hourly lectures)
``The Dirichlet problem for superdegenerate differential operators" (with Denis Bell), C.R. Acad. Sci. Paris (French Academy of Sciences, t. 327, serie I (1998), 81-86.
``The Stable Manifold Theorem for Stochastic Differential Equations" (With M. Scheutzow), The Annals of Probability, Vol. 27, No. 2, (1999), 615-652.
`` The Stable Manifold Theorem for Nonlinear Stochastic Systems with Memory I: Existence of the Semiflow" (with M. Scheutzow), Journal of Functional Analysis, 205, (2003), 271-305, (preprint available upon request).
``The Stable Manifold Theorem for Nonlinear Stochastic Systems with Memory II: The Local Stable Manifold Theorem" (with M. Scheutzow), pp. 64 , Journal of Functional Analysis, to appear (preprint available upon request).
`` Stochastic Functional Differential Equations on Manifolds " (with R. L\'eandre), {\it Probability Theory and Related Fields} 121 (2001) 1, 117-135. (preprint available upon request).
``Discrete-time Approximations of Stochastic Differential Systems with Memory" (with Yaozhong Hu and Feng Yan), pp. 71, (preprint available upon request).
``A Delayed Black and Scholes Formula" (with M. Arrioyas), (2003) pp. 19 (preprint).
``Discrete-time Approximations of Stochastic Delay Equations: The Milstein Scheme " (with Y. Hu and F. Yan), The Annals of Probability, 2004, Vol. 32, No. 1A, 265-31.
``Absolute continuity of stationary Measure-valued Processes generated by stochastic equations with interaction" (with A. Pilipenko), Theory of Stochastic Process, 2005, vol. 11(27), No.1-2, pp. 17.
``Large deviations for stochastic systems with memory'' (with T. S. Zhang), Discrete and Continuous Dynamical Systems (To appear) (2005).
`The Stable Manifold Theorem for Semilinear Stochastic Evolution Equations and Stochastic Partial Differential Equations, Part I: The Stochastic Semiflow" (with T. S. Zhang and H. Zhao), pp. 83, approx. (preprint).
`The Stable Manifold Theorem for Semilinear Stochastic Partial Differential Equations, Part II: Existence of Stable and Unstable Manifolds" (with T. S. Zhang and H. Zhao), pp. 52, approx. (preprint).
`` The Stable Manifold Theorem for Semi-Linear SPDE's" (with T. S. Zhang and H. Zhao), (2003) pp. 6. (preprint).
``Hartman-Grobman theorems along hyperbolic stationary trajectories" (with E. A. Coayla-Teran and P. R. C. Ruffino), (2005), Discrete and Continuous Dynamical Systems, pp. 17 (to appear) (preprint available upon request).