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  • 1
    Electronic Resource
    Electronic Resource
    WHEN IS THE SHORT RATE MARKOVIAN? (1994)
    Oxford, UK : Blackwell Publishing Ltd
    Mathematical finance 4 (1994), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We answer this question in the very general context of the n-factor Heath, Jarrow, and Morton model for the evolution of the term structure of interest rates, with nonrandom volatility. the answer is that a constraint is imposed on the behavior of the volatility structure. We explain the importance of this result for the design of efficient numerical algorithms for the valuation of options on the term structure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9965.1994.tb00060.x
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  • 2
    Electronic Resource
    Electronic Resource
    Furstenberg's theorem for nonlinear stochastic systems (1987)
    Springer
    Probability theory and related fields 74 (1987), S. 529-534 
    Details
    ISSN: 1432-2064
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We extend Furstenberg's theorem to the case of an i.i.d. random composition of incompressible diffeomorphisms of a compact manifold M. The original theorem applies to linear maps {X i} i ∈N on ℝ m with determinant 1, and says that the highest Lyapunov exponent $$\beta \equiv \mathop {\lim }\limits_{n \to \infty } \frac{1}{n}||X_n \circ ... \circ X_1 ||$$ is strictly positive unless there is a probability measure on the projective (m-1)-space which is a.s. invariant under the action of X i . Our extension refers to a probability measure on the projective bundle over M. We show that when our diffeomorphism is the flow of a stochastic differential equation, the criterion for β〉0 is ensured by a Lie algebra condition on the induced system on the principal bundle over M.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00363514
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  • 3
    Electronic Resource
    Electronic Resource
    Global solutions of the Navier-Stokes equation with strong viscosity (1992)
    Springer
    Annals of global analysis and geometry 10 (1992), S. 255-261 
    Details
    ISSN: 1572-9060
    Keywords: Navier-Stokes equation ; diffeomorphism groups ; geodesic flow ; 58D30 ; 35Q30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Following Ebin and Marsden the Navier-Stokes equation is viewed as a perturbation of a geodesic flow on the group of volume preserving diffeomorphisms on a compact Riemannian manifold. Existence and uniqueness of bounded solutions for all position time is shown by taking a higher order diffusion term.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00136868
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    Paper (German National Licenses)
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