Books and Articles
-Salah Mohammed
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.
- ``Opérateurs Paraboliques Hypoelliptiques Avec
Dégénérescences 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 Hörmander'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 PoincarĂ©,
Probabilites ét 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).
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October 10, 2006