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Modern Stochastics: Theory and Applications, 2020 The paper deals with a stochastic heat equation driven by an additive fractional Brownian space-only noise. We prove that a solution to this equation is a stationary and ergodic Gaussian process. These results enable us to construct a strongly consistent
Diana Avetisian, Kostiantyn Ralchenko
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Gaussian Volterra processes with power-type kernels. Part II
Modern Stochastics: Theory and Applications, 2022 In this paper the study of a three-parametric class of Gaussian Volterra processes is continued. This study was started in Part I of the present paper.
Yuliya Mishura, Sergiy Shklyar
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Harold Jeffreys's Theory of Probability Revisited
, 2009 Published exactly seventy years ago, Jeffreys's Theory of Probability (1939) has had a unique impact on the Bayesian community and is now considered to be one of the main classics in Bayesian Statistics as well as the initiator of the objective Bayes ...
Bernardo, J. M. +8 more
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On Drift Parameter Estimation in Models with Fractional Brownian Motion by Discrete Observations
Austrian Journal of Statistics, 2014 We study a problem of an unknown drift parameter estimation in a stochastic differen- tial equation driven by fractional Brownian motion. We represent the likelihood ratio as a function of the observable process.
Yuliya Mishura, Kostiantyn Ralchenko
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Understanding weak values without new probability theory [PDF]
, 2018 The physical meaning of weak values and measurements can be completely understood with Born rule and the general probability theory. It is known that the weak value of an observable $\hat A$ with post-selection $\langle F|$ may be out of the eigenvalue ...
Mochizuki, Riuji
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Convexity and robustness of the Rényi entropy
Modern Stochastics: Theory and Applications, 2021 We study convexity properties of the Rényi entropy as function of $\alpha >0$ on finite alphabets. We also describe robustness of the Rényi entropy on finite alphabets, and it turns out that the rate of respective convergence depends on initial alphabet.
Filipp Buryak, Yuliya Mishura
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The Holling Type II Population Model Subjected to Rapid Random Attacks of Predator
Journal of Applied Mathematics, 2018 We present the analysis of a mathematical model of the dynamics of interacting predator and prey populations with the Holling type random trophic function under the assumption of random time interval passage between predator attacks on prey. We propose a
Jevgeņijs Carkovs +2 more
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The splitting process in free probability theory [PDF]
, 2015 Free cumulants were introduced by Speicher as a proper analog of classical cumulants in Voiculescu's theory of free probability. The relation between free moments and free cumulants is usually described in terms of Moebius calculus over the lattice of ...
Ebrahimi-Fard, Kurusch, Patras, Frederic
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Dynamic Blockage in Indoor Reflection-Aided Sub-Terahertz Wireless Communications
IEEE Access, 2023 The sixth-generation cellular systems are expected to utilize the text sub-terahertz frequency band covering 100–300-GHz. Due to high path losses, the coverage of such systems will be limited to a few tens of meters making them suitable for indoor
Alexander Shurakov +8 more
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Assessing schematic knowledge of introductory probability theory [PDF]
, 2005 [Abstract]: The ability to identify schematic knowledge is an important goal for both assessment and instruction. In the current paper, schematic knowledge of statistical probability theory is explored from the declarative-procedural framework using ...
Birney, Damian P. +2 more
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