K. Umeno,Phys. Rev. E58 (1998) 2644 (eprint chao-dyn/9711023). Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Chaos Monte Carlo computation: a dynamical effect of random-number .. - Umeno Self-citation (Umeno) (Correct)
....systems with invariant probability measures over the infinite support Omega I = Gamma1; 1) as random numbers generators over Omega I . Such ergodic dynamical systems over the infinite support were systematically found from the multiplication formulas of tan( and its related functions [15]. We can thus use these chaotic dynamical systems for this chaos based Monte Carlo simulations over the infinite support Omega I . Let us briefly explain ergodic mappings over Omega I . As will be shown in Appendices C and D, by using the topological conjugacy relation with Chebyshev mappings T ....
....transformations F l (y) h Gamma1 ffi T l ffi h(y) 54) where h is a differential onto mapping (diffeomorphism) such that h : Gamma1; 1) Gamma1; 1) is given by h(y) 1 p 1 jyj 2ff sgn(y) for ff 0. These ergodic mappings fF l g have the same invariant probability measure [15] ae NG (y) ffjyj ff Gamma1 (1 jyj 2ff ) 55) Furthermore, as will be shown in Appendix C, we can consider the corresponding orthonormal system of functions fP l (y) j T l ffi h(y)g satisfying the same orthogonal relation as the Chebyshev orthogonal polynomials as follows: Z 1 ....
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K. Umeno,Phys. Rev. E58 (1998) 2644 (eprint chao-dyn/9711023).
Chaos Monte Carlo computation: a dynamical effect of random-number .. - Umeno Self-citation (Umeno) (Correct)
....P N j=1 f( j ) can thus approximate the integral R Omega f(x)dx with an error in the order of 1 p N when N is a large number. In this paper, we combine this ergodic principle in Monte Carlo simulations with some ideas about generating nonuniform random numbers by ergodic dynamical systems [6, 7, 8, 9]. This paper is organized as follows. In Section 2, our Monte Carlo algorithm based on ergodic (chaotic) dynamical systems is explained. In Section 3, we demonstrate that phenomena of dynamical dependency of chaos based Monte Carlo simulations are illustrated by a set of chaotic dynamical systems ....
....arbitrary multiple integrals. However, such dynamical Monte Carlo computation cannot be carried out unless their invariant densities ae(x) are explicitly known. In recent years, many chaotic dynamical systems have been derived, which have explicit invariant measures with continuous densities [8, 9]. Hence these chaotic dynamical systems can offer their applications for use as random number generators for Monte Carlo simulations. Clearly, these random number generators using chaos have strict time correlation which is not desirable for ideal random number generators. Suppose N successive ....
K. Umeno, Phys. Rev. E 55 (1997) 5280 (eprint chao-dyn/961009).
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