On the proper treatment of improper distributions [PDF]
, 2017 The axiomatic foundation of probability theory presented by Kolmogorov has been the basis of modern theory for probability and statistics. In certain applications it is, however, necessary or convenient to allow improper (unbounded) distributions, which ...
Lindqvist, Bo H., Taraldsen, Gunnar
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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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Mod-Poisson convergence in probability and number theory [PDF]
, 2009 Building on earlier work introducing the notion of "mod-Gaussian" convergence of sequences of random variables, which arises naturally in Random Matrix Theory and number theory, we discuss the analogue notion of "mod-Poisson" convergence.
Arratia +22 more
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Compact support probability distributions in random matrix theory [PDF]
, 1998 We consider a generalization of the fixed and bounded trace ensembles introduced by Bronk and Rosenzweig up to an arbitrary polynomial potential. In the large-N limit we prove that the two are equivalent and that their eigenvalue distribution coincides ...
C.W.J. Beenakker +20 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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An Analysis of Implied Volatility, Sensitivity, and Calibration of the Kennedy Model
MathematicsThe Kennedy model provides a flexible and mathematically consistent framework for modeling the term structure of interest rates, leveraging Gaussian random fields to capture the dynamics of forward rates.
Dalma Tóth-Lakits +2 more
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Gaussian Volterra processes with power-type kernels. Part I
Modern Stochastics: Theory and Applications, 2022 The stochastic process of the form \[ {X_{t}}={\int _{0}^{t}}{s^{\alpha }}\left({\int _{s}^{t}}{u^{\beta }}{(u-s)^{\gamma }}\hspace{0.1667em}du\right)\hspace{0.1667em}d{W_{s}}\] is considered, where W is a standard Wiener process, $\alpha >-\frac{1}{
Yuliya Mishura, Sergiy Shklyar
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Dynamic Topology Reconfiguration for Energy-Efficient Operation in 5G NR IAB Systems
Future InternetThe utilization of high millimeter wave (mmWave, 30–100 GHz) in 5G New Radio (NR) systems and sub-terahertz (sub-THz, 100–300 GHz) in future 6G requires dense deployments of base stations (BSs) to provide uninterrupted connectivity to the users.
Vitalii Beschastnyi +5 more
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Stability Estimates for Finite-Dimensional Distributions of Time-Inhomogeneous Markov Chains
Mathematics, 2020 This paper is devoted to the study of the stability of finite-dimensional distribution of time-inhomogeneous, discrete-time Markov chains on a general state space.
Vitaliy Golomoziy, Yuliya Mishura
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Reality and Probability: Introducing a New Type of Probability Calculus [PDF]
, 2002 We consider a conception of reality that is the following: An object is 'real' if we know that if we would try to test whether this object is present, this test would give us the answer 'yes' with certainty.
Aerts, Diederik
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