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Asymptotics for the partial sum and its maximum of dependent random variables*
Let X 1 ,…, X n be pairwise asymptotically independent or pairwise upper extended negatively dependent real-valued random variables. Under the...
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Precise large deviations for sums of random vectors with dependent components of consistently varying tails
Let {
X i = ( X 1, i ,..., X m,i ) ⊤ , i ≥ 1} be a sequence of independent and identically distributed nonnegative m -dimensional random vectors. The... -
Extremes of Gaussian processes with smooth random expectation and smooth random variance
Let ξ ( t ), t ∈ [0, T ], T > 0, be a Gaussian stationary process with expectation 0 and variance 1, and let η ( t ) and μ ( t ) be other sufficiently smooth...
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Some limit results on supremum of Shepp statistics for fractional Brownian motion
Define the incremental fractional Brownian field Z H ( τ , s ) = B H ( s + τ ) − B H ( s ), where B H ( s ) is a standard fractional Brownian motion with...
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Weak max-sum equivalence for dependent heavy-tailed random variables
We consider real-valued random variables X 1 ,…, X n with corresponding distributions F 1 ,…, F n such that X 1 ,…, X n admit some dependence structure...
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A result on precise asymptotics for largest eigenvalues of β ensembles
The paper focuses on the precise asymptotics of the largest eigenvalues of β -Hermite ensemble and β -Laguerre ensemble. In particular, we obtain a...
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Parisian ruin over a finite-time horizon
For a risk process R u ( t ) = u + ct − X ( t ), t ≥ 0, where u ≥ 0 is the initial capital, c > 0 is the premium rate and X ( t ), t ≥ 0 is an aggregate...
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On the
γ -reflected processes with fBm input*Define a γ -reflected process W γ ( t ) = Y H ( t ) − γ inf s ∈ [0. t ] Y H ( s ), t ≽ 0, γ ∈ [0, 1], with { Y H (t), t ≽ 0} a fractional Brownian motion with...
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Dynamic bivariate normal copula
Normal copula with a correlation coefficient between −1 and 1 is tail independent and so it severely underestimates extreme probabilities. By letting...
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The maxima and sums of multivariate non-stationary Gaussian sequences
Let { X k 1 , …, X kp , k ≥ 1} be a p-dimensional standard (zero-means, unit-variances) non-stationary Gaussian vector sequence. In this work, the...
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Extremes of Shepp statistics for fractional Brownian motion
Define the incremental fractional Brownian field with parameter H ∈ (0, 1) by Z H ( τ, s ) = B H ( s + τ )- B H ( s ), where B ...
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Boundary noncrossings of additive Wiener fields∗
Let { W i ( t ) , t ∈ ℝ + }, i = 1 , 2, be two Wiener processes, and let W 3 = { W 3 ( t ) , t ∈ ℝ
+ 2 } be a two-parameter Brownian sheet, all three processes... -
The limit theorems for maxima of stationary Gaussian processes with random Index
Let { X ( t ), t ≥ 0} be a standard (zero-mean, unit-variance) stationary Gaussian process with correlation function r (·) and continuous sample paths. In...
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Precise large deviations for generalized dependent compound renewal risk model with consistent variation
We investigate the precise large deviations of random sums of negatively dependent random variables with consistently varying tails. We find out the...
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Ruin probabilities with insurance and financial risks having an FGM dependence structure
We consider a discrete-time risk model, in which insurance risks and financial risks jointly follow a multivariate Farlie-Gumbel-Morgenstern...
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On Piterbarg theorem for maxima of stationary Gaussian sequences
Limit distributions of maxima of dependent Gaussian sequence are different according to the convergence rate of their correlations. For three...
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Asymptotic behavior of the convex hull of a stationary Gaussian process∗
Let X = {X ( t ) , t ∈ T} be a stationary centered Gaussian process with values in ℝ d , where the parameter set T equals ℕ or ℝ+. Let Σ ...