Gaussian Processes

Nash Twist and Gaussian Noise Measure for Isometric C1 Maps

“…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.…”

Stochastic Processes Induced by Singular Operators

“…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.…”

On the Equivalence of Multiparameter Gaussian Processes

“…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.…”

“…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.…”