美国数学学会期刊
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作者:Y. Hu
来源:[J].Theory of Probability and Mathematical Statistics, 2019, Vol.98, pp.115-126AMS
摘要:This paper studies the Schrödinger equation with fractional Gaussian noise potential of the form $ \Delta u(x)= u(x)\diamond \dot W(x)$, $ x\in D$, $ u(x)= \phi (x)$, $ x\in \partial D$, where $ \Delta $ is the Laplacian on the $ d$-dimensional Euclidean space $ \mathbb{R}^d...
作者:I. M. Bodnarchuk , V. M. Radchenko
来源:[J].Theory of Probability and Mathematical Statistics, 2019, Vol.98, pp.73-90AMS
摘要:We study the Cauchy problem for the wave equation on the plane driven by a general stochastic measure. The existence and uniqueness of a mild solution is proved. The Hölder continuity with respect to both the time and spatial variables is established for the trajectories of ...
作者:R. Gorenflo , F. Mainardi
来源:[J].Theory of Probability and Mathematical Statistics, 2019, Vol.98, pp.105-113AMS
摘要:The main purpose of this note is to point out the relevance of the Mittag-Leffler probability distribution in the so-called thinning theory for a renewal process with a queue of power law-type. This theory, formerly considered by Gnedenko and Kovalenko in 1968 without the explici...
作者:E. Azmoodeh , D. Gasbarra
来源:[J].Theory of Probability and Mathematical Statistics, 2019, Vol.98, pp.51-71AMS
摘要:In this paper, using the Stein operator $ \mathfrak{R}_\infty $ given in [Bernoulli 23 (2017), pp. 3311-3345], associated with the normal product distribution living in the second Wiener chaos, we introduce a new class of polynomials $\displaystyle \mathscr {P}_\infty := \left \{...
作者:V. V. Anh , N. N. Leonenko
来源:[J].Theory of Probability and Mathematical Statistics, 2019, Vol.98, pp.5-26AMS
摘要:This paper presents some stationary processes which are solutions of the fractional Stokes-Boussinesq-Langevin equation. These processes have reflection positivity and their correlation functions, which may exhibit the Alder-Wainwright effect or long-range dependence, are express...
作者:V. S. Koroliuk , I. V. Samoilenko
来源:[J].Theory of Probability and Mathematical Statistics, 2019, Vol.98, pp.217-227AMS
摘要:The regular as well as singular component of the asymptotic expansion of a functional constructed from a semi-Markov random evolution is found, and regularity of the initial data is shown in Theory Probab. Math. Statist. 96 (2018), 83-100. A bound for the remainder term of the as...
作者:T. Sottinen , L. Viitasaari
来源:[J].Theory of Probability and Mathematical Statistics, 2019, Vol.98, pp.199-216AMS
摘要:The $ n$th order fractional Brownian motion was introduced by Perrin et al.in IEEE Transactions on Signal Processing 49 (2001), no. 5, 1049-1059. It is the (up to a multiplicative constant) unique self-similar Gaussian process with the Hurst index $ H \in (n-1,n)$, having $ n$th ...
作者:Yu. Mishura , K. Ralchenko , G. Shevchenko
来源:[J].Theory of Probability and Mathematical Statistics, 2019, Vol.98, pp.149-170AMS
摘要:We prove the existence and uniqueness of a mild solution for a class of nonautonomous parabolic mixed stochastic partial differential equations defined on a bounded open subset $ D \subset \mathbb{R}^d$ and involving standard and fractional $ L^2(D)$-valued Brownian motions. We a...
作者:M. Sreehari
来源:[J].Theory of Probability and Mathematical Statistics, 2019, Vol.98, pp.229-242AMS
摘要:An estimate of the order of approximation in the central limit theorem for strictly stationary associated random variables with finite moments of order $ q > 2$ is obtained. A moderate deviation result is also obtained. We have a refinement of recent results in Çagin et al.,...
作者:L. I. Rusanyuk , G. M. Shevchenko
来源:[J].Theory of Probability and Mathematical Statistics, 2019, Vol.98, pp.171-181AMS
摘要:A wave equation with external forces is considered in this paper for a homogeneous string with fixed ends. The distribution of the right-hand side of the equation is symmetric $ \alpha $-stable. It is proved that the function constructed by the Fourier method is a generalized sol...

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