2007
DOI: 10.1090/mmono/120
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Gaussian Processes

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Cited by 62 publications
(89 citation statements)
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“…It is seen from the proof of Theorem 2.1 that the random Nash twist on the initial short curve f 0 to obtain an increase of r 2 (u) du 2 to the induced metric f * 0 h, leads to a process whose structure is similar to the following process (refer to [4,Theorem 6. where ℓ(s, u) is a Volterra kernel with appropriate conditions. In our case, componentwise we need a Gaussian process t 0 r(u) dW (u) and a function r ′ (u)/r(u) to replace W (t) and ℓ(s, u) in the above formula.…”
Section: Discussionmentioning
confidence: 99%
“…It is seen from the proof of Theorem 2.1 that the random Nash twist on the initial short curve f 0 to obtain an increase of r 2 (u) du 2 to the induced metric f * 0 h, leads to a process whose structure is similar to the following process (refer to [4,Theorem 6. where ℓ(s, u) is a Volterra kernel with appropriate conditions. In our case, componentwise we need a Gaussian process t 0 r(u) dW (u) and a function r ′ (u)/r(u) to replace W (t) and ℓ(s, u) in the above formula.…”
Section: Discussionmentioning
confidence: 99%
“…Still for n = 1, the papers [1] and [2] can be seen as the beginning of such a study, for certain absolutely continuous measures, and for certain singular measures respectively. For other treatments of the theory of Gaussian processes, we refer to the following books, [16], a classic, and [13] of a more recent vintage. The outline of the paper is as follows.…”
Section: Introductionmentioning
confidence: 99%
“…The question of the equivalence in law of Gaussian processes has been widely studied in the sixties-seventies (see [6], [5], [9], [14]). Recently, the problem has been reopened by several authors, due to the intensive study of the fractional Brownian and of stochastic calculus with respect to this process.…”
Section: Introductionmentioning
confidence: 99%
“…We study both Hitsuda-type (or nonanticipative) representation and Shepp-type representation. At least former seems to be closely related to the stochastic calculus and Itô's formula (see [5], Section 6.4.). Since the stochastic calculus in the multiparameter case is more complicated than in the one-parameter case, we ask ourselves if the representation theorems using stochastic integrals can yet be obtained.…”
Section: Introductionmentioning
confidence: 99%