Results 21 to 30 of about 309 (72)
Wiener measure for Heisenberg group
, 2013 In this paper, we build Wiener measure for the path space on the Heisenberg group by using of the heat kernel corresponding to the sub-Laplacian and give the definition of the Wiener integral.
Liu, Heping, Wang, Yingzhan
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Equivalence of weak and strong modes of measures on topological vector spaces [PDF]
, 2018 A strong mode of a probability measure on a normed space $X$ can be defined as a point $u$ such that the mass of the ball centred at $u$ uniformly dominates the mass of all other balls in the small-radius limit.
Lie, Han Cheng, Sullivan, T. J.
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Duality of measure and category in infinite‐dimensional separable Hilbert space ℓ2
International Journal of Mathematics and Mathematical Sciences, Volume 30, Issue 6, Page 353-363, 2002., 2002 We prove that an analogy of the Oxtoby duality principle is not valid for the concrete nontrivial σ‐finite Borel invariant measure and the Baire category in the classical Hilbert space ℓ2.
Gogi Pantsulaia
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Chaos decomposition and gap renormalization of brownian self-intersection local times [PDF]
, 2015 We study the chaos decomposition of self-intersection local times and their regularization, with a particular view towards Varadhan's renormalization for the planar Edwards ...
Bornales, Jinky +2 more
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A change of scale formula for Wiener integrals of cylinder functions on the abstract Wiener space II
International Journal of Mathematics and Mathematical Sciences, Volume 25, Issue 4, Page 231-237, 2001., 2001 We show that for certain bounded cylinder functions of the form F(x)=μˆ((h1,x)∼,…,(hn,x)∼), x ∈ B where μˆ:ℝn→ℂ is the Fourier‐transform of the complex‐valued Borel measure μ on ℬ(ℝn), the Borel σ‐algebra of ℝn with ‖μ‖ < ∞, the analytic Feynman integral of F exists, although the analytic Feynman integral, limz→−iqIaw(F;z)=limz→−iq(z/2π) n/2∫ℝnf(u→)exp{
Young Sik Kim
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On Wigner transforms in infinite dimensions
, 2015 We investigate the Schr\"odinger representations of certain infinite-dimensional Heisenberg groups, using their corresponding Wigner transforms.Comment: 15 ...
Beltita, Daniel +2 more
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Conditional generalized analytic Feynman integrals and a generalized integral equation
International Journal of Mathematics and Mathematical Sciences, Volume 23, Issue 11, Page 759-776, 2000., 2000 We use a generalized Brownian motion process to define a generalized Feynman integral and a conditional generalized Feynman integral. We then establish the existence of these integrals for various functionals. Finally we use the conditional generalized Feynman integral to derive a Schrödinger integral equation.
Seung Jun Chang +2 more
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Coupling of Brownian motions in Banach spaces
, 2017 Consider a separable Banach space $ \mathcal{W}$ supporting a non-trivial Gaussian measure $\mu$. The following is an immediate consequence of the theory of Gaussian measure on Banach spaces: there exist (almost surely) successful couplings of two ...
Candellero, Elisabetta +1 more
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Relationships among transforms, convolutions, and first variations
International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 1, Page 191-204, 1999., 1999 In this paper, we establish several interesting relationships involving the Fourier‐Feynman transform, the convolution product, and the first variation for functionals F on Wiener space of the form where 〈αj, x〉 denotes the Paley‐Wiener‐Zygmund stochastic integral .
Jeong Gyoo Kim +3 more
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Inequalities for the Gaussian measure of convex sets
, 2017 This note presents families of inequalities for the Gaussian measure of convex sets which extend the recently proven Gaussian correlation inequality in various ...
Tehranchi, Michael R.
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