Tail Probabilities of Gaussian Suprema and Laplace Transform M.A. Lifshits Let {xt , t ∈ T } be a bounded Gaussian random field and Z = supT xt . We investigate the large deviations by means of the Laplace transform Ψp (λ) = E exp{λz p },
1 ≤ p < 2.
We derive for large r the asymptotical equivalence P {Z ≥ r} ∼ ABC with A = (2 − p)1/2 Ψp
²
r2−p − dr1−p pσ 2
³ ,
º » (2 − p)r2 d(p − 1)r d2 B = exp − − + 2 , 2pσ 2 pσ 2 2σ ² ³ r−d C =1−Φ , σ where d and σ are some important numeric parameters of the field x and Φ is the distribution function of the standard normal law. We apply this relation to the investigation of the Gaussian measure of large balls in the space `p in order to generalise some recent results due to Linde and author. The broad range of possible types of behavior of large deviations is under consideration and some of them turn out to be unusual.
Tail Probabilities of Gaussian Suprema and Laplace ...
where d and Ï are some important numeric parameters of the field x and Φ is the distribution function of the standard normal law. We apply this relation to the investigation of the Gaussian measure of large balls in the space lp in order to generalise some recent results due to Linde and author. The broad range of possible ...
E Xk = 0 and EX2 k = Ï2 k for all k. Hoeffding 1963, Theorem 3, proved that. P{Mn ⥠nt} ⤠Hn(t, p), H(t, p) = `1 + qt/p´ p+qt`1 â t´qâqt with q = 1. 1 + Ï2 , p = 1 â q, ...
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M.A. Lifshits. The behavior of tail probabilities P{S ⤠r}, r â 0, is investigated, where S is a series S = â λjZj generated by some sequence of positive numbers ...
corresponding integral covariance operator. We find the exact val- ues of such norms for some important classes of Gaussian fields on the square generalizing ...
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Page 1. Probabilities of Randomly Centered Small Balls and. Quantization in Banach Space. S.Dereich and M.A. Lifshits. We investigate the Gaussian small ball probabilities with ran- dom centers, find their deterministic a.s.-equivalents and establish
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We obtain evaluations of probabilities of shifted small balls for the centered. Poisson process by making use of a density argument which, for the Poisson process, plays a role similar to that of the Cameron-Martin formula for the. Wiener process. 1.
networks found that Cauchy mutation had better performance than Gaussian ... network training performance using a certain perturbation function does not.
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Page 1 of 23. devsamajcollege.blogspot.in Sanjay Gupta, Dev Samaj College For Women, Ferozepur City. INVERSE LAPLACE TRANSFORMS. CHAPTER EXERCISE 6.4 - 6. Q.1. Page 1 of 23. Page 1 of 23. Page 2 of 23. devsamajcollege.blogspot.in Sanjay Gupta, Dev Sa
Page 1 of 18. Sanjay Gupta, Dev Samaj College For Women, Ferozepur City devsamajcollege.blogspot.in. LAPLACE TRANSFORMS. EXERCISE 5.3 CHAPTER - 5. Q.1. Q.2. Page 1 of 18. Page 1 of 18. Page 2 of 18. devsamajcollege.blogspot.in Sanjay Gupta, Dev Samaj
A conventional technique for simulating a Gaussian time history generates the Gaussian signal by summing up a number of sine waves with random phase angles and either deterministic or random amplitudes. After this sim- ulated process has been used as
we maintain a distribution over alternative weight vectors, rather than committing to ..... We implemented in matlab a Hildreth-like algorithm (Cen- sor and Zenios ...
Ba Tuong Vo. Ba-Ngu Vo. Department of ... The University of Western Australia ...... gineering) degrees with first class hon- .... Orlando, Florida [6235-29],. 2006.
Section 4.2 describes the databases and the experimental ... presents our results on this database. ... We use the limited memory BFGS algorithm [7] with the.
separable samples, we can relax the inequality constraints by introducing a slack variable ξi for each point xi and aug- menting the objective function with a ...