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...