Results 1 to 10 of about 3,092 (108)
Necessary and Sufficient Conditions for H\"older Continuity of Gaussian Processes [PDF]
, 2013 The continuity of Gaussian processes is extensively studied topic and it culminates in the Talagrand's notion of majorizing measures that gives complicated necessary and sufficient conditions.
Azmoodeh, Ehsan +3 more
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The random Wigner distribution of Gaussian stochastic processes with covariance in S0(ℝ2d)
Journal of Function Spaces, Volume 3, Issue 2, Page 163-181, 2005., 2005 The paper treats time‐frequency analysis of scalar‐valued zero mean Gaussian stochastic processes on ℝd. We prove that if the covariance function belongs to the Feichtinger algebra S0(ℝ2d) then: (i) the Wigner distribution and the ambiguity function of the process exist as finite variance stochastic Riemann integrals, each of which defines a stochastic
Patrik Wahlberg, Hans Feichtinger
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An extension of the Clark‐Ocone formula
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 28, Page 1463-1476, 2004., 2004 A white noise proof of the classical Clark‐Ocone formula is first provided. This formula is proven for functions in a Sobolev space which is a subset of the space of square‐integrable functions over a white noise space. Later, the formula is generalized to a larger class of operators.
Said Ngobi, Aurel Stan
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Baxter's inequality for fractional Brownian motion-type processes with Hurst index less than 1/2 [PDF]
, 2008 The aim of this paper is to prove an analogue of Baxter's inequality for fractional Brownian motion-type processes with Hurst index less than 1/2. This inequality is concerned with the norm estimate of the difference between finite- and infinite-past ...
Inoue, Akihiko +2 more
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New formulas concerning Laplace transforms of quadratic forms for general Gaussian sequences
International Journal of Stochastic Analysis, Volume 15, Issue 4, Page 309-325, 2002., 2002 Various methods to derive new formulas for the Laplace transforms of some quadratic forms of Gaussian sequences are discussed. In the general setting, an approach based on the resolution of an appropriate auxiliary filtering problem is developed; it leads to a formula in terms of the solutions of Volterra‐type recursions describing characteristics of ...
M. L. Kleptsyna, A. Le Breton, M. Viot
wiley +1 more source
International Journal of Stochastic Analysis, Volume 14, Issue 3, Page 215-226, 2001., 2001 The optimal filtering problem for multidimensional continuous possibly non‐Markovian, Gaussian processes, observed through a linear channel driven by a Brownian motion, is revisited. Explicit Volterra type filtering equations involving the covariance function of the filtered process are derived both for the conditional mean and for the covariance of ...
M. L. Kleptsyna, A. Le Breton
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Fredholm representation of multiparameter Gaussian processes with applications to equivalence in law and series expansions [PDF]
, 2015 We show that every multiparameter Gaussian process with integrable variance function admits a Wiener integral representation of Fredholm type with respect to the Brownian sheet.
Sottinen, Tommi, Viitasaari, Lauri
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Self‐similar processes in collective risk theory
International Journal of Stochastic Analysis, Volume 11, Issue 4, Page 429-448, 1998., 1998 Collective risk theory is concerned with random fluctuations of the total assets and the risk reserve of an insurance company. In this paper we consider self‐similar, continuous processes with stationary increments for the renewal model in risk theory. We construct a risk model which shows a mechanism of long range dependence of claims.
Zbigniew Michna
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An approach to the stochastic calculus in the non‐Gaussian case
International Journal of Stochastic Analysis, Volume 8, Issue 4, Page 361-370, 1995., 1995 We introduce and study a class of operators of stochastic differentiation and integration for non‐Gaussian processes. As an application, we establish an analog of the Itô formula.
Andrey A. Dorogovtsev
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Square variation of Brownian paths in Banach spaces
International Journal of Mathematics and Mathematical Sciences, Volume 5, Issue 3, Page 605-607, 1982., 1982 It is known that if {W(t), 0 ≤ t ≤ 1} is a standard Brownian motion in ℝ then almost surely. We generalize this celebrated theorem of Levy to Brownian motion in real separable Banach spaces.
Mou-Hsiung Chang
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