1,058 research outputs found
Properties of Hida processes on 2. 1. N-Hida processes
No full textIf E is an ordered set, we study the processes Yt, t [set membership, variant] E, for which the vectorial spaces t generated by all the conditional expectations E(Ys[beta]t) for s >= t have finite dimensions d(t)Hida processes Multiparameter processes Markov property Prediction Interpolation
QUANTUM-THEORY IN TERMS OF WHITE NOISE
No full textHIDA T, Streit L. QUANTUM-THEORY IN TERMS OF WHITE NOISE. NAGOYA MATHEMATICAL JOURNAL. 1977;68(DEC):21-34
WHITE NOISE-ANALYSIS AND ITS APPLICATION TO FEYNMAN INTEGRAL
No full textStreit L, HIDA T. WHITE NOISE-ANALYSIS AND ITS APPLICATION TO FEYNMAN INTEGRAL. LECTURE NOTES IN MATHEMATICS. 1983;1033:219-226
Abstract Wiener Space Approach to Hida Calculus (Brownian Motion).
No full textLet be the Schwartz space of rapidly decreasing real functions on The dual space {\cal S}\sp\ast of consists of tempered distributions. The inclusion maps {\cal S}\subset{\rm L\sp2(I\!R)}\subset{\cal S}\sp\ast are continuous. Hida\u27s theory of Brownian and generalized Brownian functionals is the study of functionals defined on {\cal S}\sp\ast. In this dissertation, the triple {\cal S}\subset{\rm L\sp2(I\!R)}\subset{\cal S}\sp\ast is replaced by an abstract Wiener space {\rm B}\sp\ast H B and an abstract version of Hida\u27s theory is developed. The Gaussian measure on {\cal S}\sp\ast in Hida\u27s calculus is replaced by the standard Gaussian measure on the space B. The {\cal S}\sp\ast valued curve \{\delta\sb{\rm t}; {\rm t \in I\!R}\} in Hida calculus is replaced by a B-valued curve The coordinate system, differential operator, and Laplacian operators with respect to in the Abstract Wiener space setup. Similar properties and theorems as in Hida calculus are obtained
Finite Dimensional Hida Distributions
No full textAbstractLet E be a real Hilbert space and A a densely defined linear operator on E satisfying certain conditions. Let E ⊂ E ⊂ E* be the Gel′fand triple arising from E and A. Let μ denote the standard Gaussian measure on E* and let (L2) = L2(μ). The Wiener-Itô decomposition theorem for (L2) and the second quantization operator Γ(A)* can be used to introduce a Gel′fand triple (E) ⊂ (L2) ⊂ (E)*. The elements in (E)* and (E) are called Hida distributions and test functions, respectively. A Hida distribution φ is defined to be finite dimensional if there exists a finite dimensional subspace V of E such that φbelongs to the (E)*-closure of polynomials in〈·, e1〉, 〈·, e2〉, ..., 〈·, ek〉, where the ej′s span V. In this case, δ is said to be based on V. A test function φ is said to be finite dimensional if φ ∈ (E) and there exists a finite dimensional subspace V of E such that φ is based on V. Several characterization theorems for the finite dimensional Hida distributions and test functions are obtained. Approximation theorems of Hida distributions and test functions by finite dimensional Hida distributions and test functions, respectively, are proved. The characterization theorems are based on the Gel′fand triple H(Rk) ⊂ H0(Rk) ⊂ (H*(Rk) arising from the standard Gaussian measure on Rk and the operator e−tL, where L = Δ - ∑kj=1uj ∂/∂uj. Properties and characterizations of elements in H(Rk)(Rk) and H*(Rk) are also obtained. The classical Fourier transform on the space S*(Rk) of tempered distributions is extended to the space H*(Rk). The generalized Itô formula is proved for F(B(t)) with F ∈ H*(Rk)
DIRICHLET FORMS AND WHITE NOISE-ANALYSIS
No full textHIDA T, POTTHOFF J, Streit L. DIRICHLET FORMS AND WHITE NOISE-ANALYSIS. COMMUNICATIONS IN MATHEMATICAL PHYSICS. 1988;116(2):235-245
THE VACUUM OF THE HOEGH-KROHN MODEL AS A GENERALIZED WHITE NOISE FUNCTIONAL
No full textAlbeverio S, HIDA T, POTTHOFF J, Streit L. THE VACUUM OF THE HOEGH-KROHN MODEL AS A GENERALIZED WHITE NOISE FUNCTIONAL. PHYSICS LETTERS B. 1989;217(4):511-514
Boson Fock representations of stochastic processes
No full textA, classification theory of quantum stationary processes similar to the corresponding theory for classical
stationary processes is presented, Our main result is the classificatio
Rb–Sr Geochronology of the Hida metamorphic belt, Japan
No full text Rb–Sr whole-rock and mineral isochron ages have been determined for metamorphic and granitic rocks of the Hida metamorphic belt. The results indicate that an extensive metamorphic event together with plutonic activity took place within the belt during the latest Paleozoic – early Mesozoic period. The older ages of 220–250 m.y. represent an earlier phase of the metamorphism, whereas the younger ages of 170–180 m.y. represent a later phase. The Funatsu granitic rocks yielded a whole-rock isochron age of 176 m.y. with an initial 87Sr/86Sr ratio of 0.7056. This age is believed to indicate the time of original emplacement, and the rocks are considered to represent late-kinematic intrusion in the Hida belt.Some information on the middle Paleozoic metamorphism in the Hida Mountains was obtained from the isochron study. The whole-rock isochron age of 412 m.y. for the metamorphic rocks of the Fujibashi area may be considered, although not confirmed, to indicate the time of older metamorphism. The Omi Schist of the Circum–Hida crystalline schist belt, which belongs to the glaucophanitic type of metamorphism, gave a mineral isochron age of 350 m.y. thereby providing evidence of mid-Paleozoic metamorphism.The initial 87Sr/88Sr ratios for the whole-rock samples of the Hida metamorphic belt are found to be generally low, i.e. 0.705–0.708. This is especially so for the metamorphic rocks from the northern part of the belt where the lowest values were found. </jats:p
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