This paper analyzes the information disclosure problems originated in economics through the lens of information theory. Such problems are radically different from the conventional communication ...paradigms in information theory since they involve different objectives for the encoder and the decoder, which are aware of this mismatch and act accordingly. This leads, in our setting, to a hierarchical communication game, where the transmitter announces an encoding strategy with full commitment, and its distortion measure depends on a private information sequence whose realization is available at the transmitter. The receiver decides on its decoding strategy that minimizes its own distortion based on the announced encoding map and the statistics. Three problem settings are considered, focusing on the quadratic distortion measures, and jointly Gaussian source and private information: compression, communication, and the simple equilibrium conditions without any compression or communication. The equilibrium strategies and associated costs are characterized. The analysis is then extended to the receiver side information setting and the major changes in structure of optimal strategies are identified. Finally, an extension of the results to the broader context of decentralized stochastic control is presented.
In this paper a new stochastic-heuristic methodology for the optimisation of the electrical supply of stand-alone (off-grid) hybrid systems (photovoltaic-wind-diesel with battery storage) is shown. ...The objective is to minimise the net present cost of the system. The stochastic optimisation is developed by means of Monte Carlo simulation, which takes into account the uncertainties of irradiation, temperature, wind speed and load (correlated Gaussian random variables), using their probability density functions and the variance-covariance matrix. Also the uncertainty of diesel fuel price inflation rate was considered. The heuristic approach uses genetic algorithms to obtain the optimal system (or a solution near the optimal) in a reasonable computation time. This methodology includes an accurate weighted Ah-throughput battery model with several control variables, which can be set in the modern battery controllers or inverter/chargers with State of Charge control. A case study is analysed as an example of the application of this methodology, obtaining the stochastic optimisation an optimal system similar to the one obtained by the deterministic optimisation. It is recommended to perform first the deterministic optimisation (with low computation time), then the search space should be reduced and finally the stochastic optimisation can be obtained in a reasonable computation time.
•Optimisation of components and control variables of stand-alone hybrid systems.•Probabilistic approach by Monte Carlo simulation combined with genetic algorithms.•Inputs are probability density functions of metheorological variables and load.•Correlations of irradiation, temperature, wind speed and load are considered.•Outputs are probability density functions of the different variables calculated.
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For classical finite time horizon stopping problems driven by a Brownian motion V(t,x)=supt≤τ≤0E(t,x)g(τ,Wτ),we derive a new class of Fredholm type integral equations for the stopping set. For a ...large class of discounted problems, we show by analytical arguments that the equation uniquely characterizes the stopping boundary of the problem. Regardless of uniqueness, we use the representation to rigorously find the limit behavior of the stopping boundary close to the terminal time. Interestingly, it turns out that the leading-order coefficient is universal for wide classes of problems. We also discuss how the representation can be used for numerical purposes.
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The long-standing Gaussian product inequality (GPI) conjecture states that E∏j=1n|Xj|αj≥∏j=1nE|Xj|αj for any centered Gaussian random vector (X1,…,Xn) and any non-negative real numbers αj, j=1,…,n. ...In this note, we prove a novel “opposite GPI” for centered bivariate Gaussian random variables when −1<α1<0 and α2>0: E|X1|α1|X2|α2≤E|X1|α1E|X2|α2. This completes the picture of bivariate Gaussian product relations.
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Explicit formulae for the product moments of multivariate Gaussian random variables are derived. The formulae we have discovered are more compact than other well-known ones and allow us to instantly ...evaluate any term of the product moments.
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This letter considers the distribution of product for two correlated real Gaussian random variables with nonzero means and arbitrary variances, which arises widely in radar and communication ...societies. We determine the exact probability density function (PDF) in terms of an infinite sum of modified Bessel functions of second kind, which includes some existent results, i.e., zero-means and/or independent variables, as special cases. Then, we study the approximation error and convergence rate when finite summations are exploited in practice. Finally, we evaluate the PDF behaviors of the derived expression as well as the Monte Carlo simulations.
We investigate Ornstein-Uhlenbeck operator which serves as an important tool with application in many fields, including sensitivity analysis involving Levy processes using ´ Malliavin calculus. Some ...processes with multivariate random variables have feature of correlation among the random variables. Hence, there is need to obtain the Ornstein-Uhlenbeck operator for such phenomenon. This paper was therefore designed to derive the Ornstein-Uhlenbeck operator for correlated multivariate random variables.
In this letter, we derive new results for the statistics of the ratio of two complex Gaussian random variables (RVs), where the numerator and denominator may have arbitrary means and are possibly ...correlated. Exact expressions are derived for the joint probability density function (pdf) of the real and imaginary parts, for the joint pdf of the amplitude and phase, and also for the joint characteristic function (cf) of the real and imaginary parts, which generalize the existing results. Then, we show an example application of the derived pdf to the symbol error probability (SEP) analysis for a single antenna communication system with imperfect channel state information (ICSI).
Let $f$ be an analytic function in $\{z: |z|<R\}$ of the form $f(z)=\sum\limits_{n=0}^{+\infty}a_n z^n$. In the paper, we consider the Wiman-type inequality for random analytic functions of the form ...$f(z,\omega)=\sum\limits_{n=0}^{+\infty}Z_n(\omega)a_nz^n$, where $(Z_n)$ is a sequence on the Steinhaus probability space of real independent centered sub-Gaussian random variables, i.e. $(\exists D>0)(\forall k\in\mathbb{N})(\forall \lambda\in\mathbb{R})\colon \mathbf{E}(e^{\lambda Z_k})\leq e^{D \lambda^2}$, and such that $(\exists\beta>0)(\exists n_0\in\mathbb{N})\colon \inf\limits_{n\geq n_0}\mathbf{E}|Z_n|^{-\beta}<+\infty.$
It is proved that for every $\delta>0$ there exists a set $E(\delta)\subset 0,R)$ of finite $h$-logarithmic measure (i.e. $\int\nolimits_{E}h(r)d\ln r<+\infty$) such that almost surely for all $r\in(r_0(\omega),R)\backslash E$ we have \ M_f(r,\omega):=\max\big\{|f(z,\omega)|\colon |z|=r\big\}\leq \sqrt{h(r)}\mu_f(r)\Big(\ln^3h(r)\ln\{h(r)\mu_f(r)\}\Big)^{1/4+\delta}, \ where $h(r)$ is any fixed continuous non-decreasing function on $0;R)$ such that $h(r)\geq2$ for all $r\in (0,R)$ and $\int^R_{r_{0}} h(r) d\ln r =+\infty$ for some $r_0\in(0,R)$.
In this letter, we derive the exact joint probability density function (pdf) of the amplitude and phase of the product of two correlated non-zero mean complex Gaussian random variables with arbitrary ...variances. This distribution is useful in many problems, for example radar and communication systems. We determine the joint pdf in terms of an infinite summation of modified Bessel functions of the first and second kinds, which generalizes the existing results. The truncation error is also studied when a truncated sum is employed. Finally, we evaluate the derived expressions through numerical experiments.
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