Integral representation with adapted continuous integrand with respect to fractional Brownian motion [PDF]
, 2014 We show that if a random variable is a final value of an adapted Holder continuous process, then it can be represented as a stochastic integral with respect to fractional Brownian motion, and the integrand is an adapted process, continuous up to the ...
Shevchenko, Georgiy, Viitasaari, Lauri
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On the second moment of the number of crossings by a stationary Gaussian process
, 2006 Cram\'{e}r and Leadbetter introduced in 1967 the sufficient condition \[\frac{r''(s)-r''(0)}{s}\in L^1([0,\delta],dx),\qquad \delta>0,\] to have a finite variance of the number of zeros of a centered stationary Gaussian process with twice differentiable ...
Kratz, Marie F., León, José R.
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Gaussian lower bounds for the density via Malliavin calculus [PDF]
, 2019 In this paper, based on a known formula, we use a simple idea to get a new representation for the density of Malliavin differentiable random variables.
Dung, Nguyen Tien
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The Cameron-Martin Theorem for (p-)Slepian processes
, 2015 We show a Cameron-Martin theorem for Slepian processes $W_t:=\frac{1}{\sqrt{p}}(B_t-B_{t-p}), t\in [p,1]$, where $p\geq \frac{1}{2}$ and $B_s$ is Brownian motion.
Bischoff, Wolfgang, Gegg, Andreas
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Dependence modeling in general insurance using local Gaussian correlations and hidden Markov models
Dependence ModelingThis article introduces a hybrid framework that combines local Gaussian correlation (LGC) with hidden Markov models (HMMs) to model dynamic and nonlinear dependencies in general insurance claims, thereby addressing the limitations of static copula ...
Afazali Zabibu +4 more
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On the Equality of Sharp and Germ - Fields for Gaussian Processes and Fields [PDF]
, 2004 2000 Mathematics Subject Classification: 60G15, 60G60; secondary 31B15, 31B25, 60H15We investigate the relationship between the sigma-field and the infinitesimal or germ sigma ...
Pitt, Loren D., Robeva, Raina S.
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A Universality Property of Gaussian Analytic Functions [PDF]
, 2010 We consider random analytic functions defined on the unit disk of the complex plane as power series such that the coefficients are i.i.d., complex valued random variables, with mean zero and unit variance.
Ledoan, Andrew +2 more
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Random determinants, mixed volumes of ellipsoids, and zeros of Gaussian random fields [PDF]
, 2012 Consider a $d\times d$ matrix $M$ whose rows are independent centered non-degenerate Gaussian vectors $\xi_1,...,\xi_d$ with covariance matrices $\Sigma_1,...,\Sigma_d$. Denote by $\mathcal{E}_i$ the location-dispersion ellipsoid of $\xi_i:\mathcal{E}_i={
Kabluchko, Zakhar, Zaporozhets, Dmitry
core
Intervention in Ornstein-Uhlenbeck SDEs [PDF]
, 2013 We introduce a notion of intervention for stochastic differential equations and a corresponding causal interpretation. For the case of the Ornstein-Uhlenbeck SDE, we show that the SDE resulting from a simple type of intervention again is an Ornstein ...
Sokol, Alexander
core
Higher-order expansions of powered extremes of normal samples
, 2016 In this paper, higher-order expansions for distributions and densities of powered extremes of standard normal random sequences are established under an optimal choice of normalized constants.
Ling, Chengxiu, Zhou, Wei
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