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Showing 1 to 20 of 34 for “"weak convergence"”.
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Weak convergence and the prediction process
We first consider convergence in law of measurable processes with a general parameter set and a state space. To this end, we need to investigate topological properties of the space of measurable functions which is the paths space of measurable processes. Also a characterization of compact sets in …
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A strong maximum principle for reaction-diffusion systems and a weak convergence scheme for reflected stochastic differential equations by Lawrence Christopher Evans.
… of the solution to such a reflected SDE is the weak limit of the distribution of the solutions of the reflected SDEs one gets by replacing the driving Brownian motion by its N-dyadic linear interpolation. In particular, we can infer geometric properties of the solutions to a Stratonovich …
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Tikimybinių matų charakteringosios transformacijos /
It is obtained, that the weak convergence in the sense of X implies the convergence of characteristic transforms, and, on the contrary, if the characteristic transforms converge weakly to the functions contiuous at zero, the from this the weak convergence in the sense of X for the probability …
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Two applications of U-Statistic type processes to detecting failures in risk models and structural breaks in linear regression models
… on U-statistic type process, a number of weak convergence results regarding three weighted partial sum processes are established. It is shown that these partial sum processes share certain invariance properties; estimation risk does not affect their weak convergence results and they are …
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Trimatė ribinė teorema periodinėms dzeta funkcijoms /
… three-dimensional limits theorem in the sense of weak convergence of probability measures for the periodic zeta-functions. The result formulated by theorem.
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Asymptotic Properties Of Markov Modulated Sequences With Fast And Slow Time Scales
… scaling. Our main effort focuses on obtaining weak convergence and strong approximation results.</p>
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Two-Time-Scale Systems In Continuous Time With Regime Switching And Their Applications
… and mean of martingale formulation to show a weak convergence result. </p> <p>The first chapter is devoted to the study of stochastic Li´enard equations with random switching. The motivation of our study stems from modeling of complex systems in which both continuous dynamics and discrete …
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On long time dynamic and singularity formation of NLS
… simultaneously. In the second part, we show weak convergence to ground state for certain radial blow up solutions to NLS at well chosen time sequence. We also include a lecture note on concentration compactness. Concentration compactness is one of the main tool we use in the second part of …
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On Switching Diffusions: The Feynman-Kac Formula And Near-Optimal Controls
… representations for solutions of certain weakly coupled elliptical systems of partial differential equations. The formulas are verified for the boundary value problem, the initial value problem, and the initial boundary value problem. Second, we show the existence of near-optimal controls …
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Invariance Principles for Random Processes Generated by Extrema and Partial Sums of Random Variables
… the strong invariance principle yields several weak convergence results for extremal processes. This differs from the case of partial sums in that Strassen's result does not yield the central limit theorem. By a similar procedure, we also obtain a strong invariance principle for point processes …
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LIMIT THEOREMS FOR FUNCTIONS OF MARGINAL QUANTILES AND ITS APPLICATION.
… leads to the central limit theorem. A weak convergence to a Gaussian process using equicontinuity of functions is indicated. The conditions ,under which these results are established.Simulation results of the Marshall-Olkin bivariate exponential distribution and the …
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Sparse functional regression models: minimax rates and contamination
… the sensitive point. The minimax rate of convergence for estimating the parameters in sparse functional linear regression is derived. It is shown that the optimal rate for estimating the sensitive point depends on the roughness of the predictor function, which is quantified by a …
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Stochastic Approximation Algorithms With Applications To Particle Swarm Optimization, Adaptive Optimization, And Consensus
… type iterative algorithm. Then we analyze its convergence using weak convergence method. It is proved that a suitably scaled sequence of swarms converge to the solution of an ordinary differential equation. We also establish certain stability results. Moreover, convergence rates are ascertained …
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Adaptive Stochastic Systems: Estimation, Filtering, And Noise Attenuation
… Mean-square error bounds are established, and weak convergence methods are employed to show the convergence of suitably interpolated sequences of estimates to solutions of systems of ordinary and stochastic differential equations with regime switching.</p> <p>Next we consider problems in noise …
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Convex hulls of planar random walks
… limits. We deduce these results from weak convergence statements for the convex hulls of random walks to scaling limits defined in terms of convex hulls of certain Brownian motions. We give bounds that confirm that the limiting variances in our results are non-zero.
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Numerical methods for problems arising in risk management and insurance
… of actuarial science, and based on the theory of weak convergence of probability measures, the convergence of the approximating sequences is obtained. In fact, under very broad conditions, we prove that the sequences of approximating Markov chain, the cost functions, and the value functions all …
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Kac's random walk and coupon collector's process on posets
… an upper bound mix = O (n2.5 log n) for the weak convergence which is close to the trivial lower bound [Omega] (n2). This improves the upper bound O (n4 log n) by Diaconis and SaloffCoste 1131. The proof is a variation on the coupling technique we develop to bound the mixing time for compact …
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Nonlinear filtering of high dimensional, chaotic, multiple timescale correlated systems
… main result is that we can retrieve a rate of convergence and that there is a metric generating the topology of weak convergence, such that the marginal filter converges to the averaged filter at the given rate in the limit of large timescale separation. The proof uses a probabilistic …
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Fractional stochastic volatility models: approximation, calibration and hedging
… we first prove a Donsker type theorem for the convergence to fractional Ornstein-Uhlenbeck process. With that theorem we prove the weak convergence of the scheme to the log-price process. We also take into account the correlation between the volatility and the stock process, which is also …
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Fluid-structure interaction in noisy nonlinear systems
… flutter instability). Numerical results show the convergence in law of the critical modes of the original system to the critical modes resulting from the homogenized one-dimensional stochastic nonlinear system for both parametric and combined excitations; in turn revealing the weak convergence of …
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