Weak Convergence of Random Polygonal Lines to a Wiener Process

1986 ◽  
Vol 30 (2) ◽  
pp. 225-234 ◽  
Author(s):  
V. M. Kruglov
Keyword(s):  
Weak Convergence ◽  
Wiener Process

Weak convergence of discrete scattering processes

1991 ◽  
Vol 23 (4) ◽  
pp. 733-750 ◽  
Author(s):  
Lajos Horváth
Keyword(s):  
Weak Convergence ◽  
Wiener Process ◽  
Scattering Process

We show that the discrete scattering process converges weakly to a time-changed Wiener process.

On the weak convergence of U-statistic processes, and of the empirical process

1978 ◽  
Vol 83 (2) ◽  
pp. 269-272 ◽  
Author(s):  
R. M. Loynes
Keyword(s):  
Weak Convergence ◽  
Wiener Process ◽  
Empirical Process ◽  
Convergence Result ◽  
The Other ◽  
Direct Argument ◽  
Random Functions ◽  
Martingale Theorem ◽  
The Relationship ◽  
Special Case

1. Summary and introductionIn (5) a weak convergence result for U-statistics was obtained as a special case of a reverse martingale theorem; in (7) Miller and Sen obtained another such result for U-statistics by a direct argument. As they stand these results are not very closely connected, since one is concerned with U-statistics Uk for k ≥ n, while the other deals with Uk for k ≤ n, but if one instead thinks of k as unrestricted and transforms the random functions Xn which enter into one of these results into new functions Yn by setting Yn(t) = tXn(t−1) one finds that the Yn are (aside from variations in interpolated values) just the functions with which the other result is concerned. As the limiting Wiener process W is well-known to have the property that tW(t−1) is another Wiener process it is not too surprising that both results should hold, and part of the purpose of this paper is to provide a general framework within which the relationship between these results will become clear. A second purpose is to illustrate the simplification that the martingale property brings to weak convergence studies; this is shown both in the U-statistic example and in a new proof of the convergence of the empirical process.

scholarly journals Weak Convergence of Markov Random Evolutions in a Multidimensional Space

2012 ◽  
Vol 2012 ◽  
pp. 1-19
Author(s):  
Igor V. Samoilenko
Keyword(s):  
Weak Convergence ◽  
Singular Perturbation ◽  
Diffusion Process ◽  
Wiener Process ◽  
Multidimensional Space ◽  
Random Evolution ◽  
Relative Compactness ◽  
Markov Random ◽  
Random Evolutions

We study Markov symmetrical and nonsymmetrical random evolutions in Rn. Weak convergence of Markov symmetrical random evolution to Wiener process and of Markov non-symmetrical random evolution to a diffusion process with drift is proved using problems of singular perturbation for the generators of evolutions. Relative compactness in DRn×Θ[0,∞) of the families of Markov random evolutions is also shown.

Weak convergence of discrete scattering processes

1991 ◽  
Vol 23 (04) ◽  
pp. 733-750 ◽  
Author(s):  
Lajos Horváth
Keyword(s):  
Weak Convergence ◽  
Wiener Process ◽  
Scattering Process

We show that the discrete scattering process converges weakly to a time-changed Wiener process.

Common Fixed Points in Modular Spaces

2018 ◽  
pp. 502 ◽  
Author(s):  
Salwa Salman Abed ◽  
Karrar Emad Abdul Sada
Keyword(s):  
Fixed Point ◽  
Weak Convergence ◽  
Fixed Point Theorems ◽  
Active Role ◽  
Common Fixed Points ◽  
Weakly Compact ◽  
Expansive Mapping ◽  
Modular Spaces ◽  
Opial’S Property ◽  
Common Fixed Point Theorems

     In this paper,there are   new considerations about the dual of a modular spaces and weak convergence. Two common fixed point theorems for a -non-expansive mapping defined on a star-shaped weakly compact subset are proved,  Here the conditions of affineness, demi-closedness and Opial's property play an active role in the proving our results.  

Forecasting based on spectral time series analysis: prediction of the Aurubis stock price

2020 ◽  
Vol 17 (4) ◽  
pp. 215-227
Author(s):  
Julia Babirath ◽  
Karel Malec ◽  
Rainer Schmitl ◽  
Kamil Maitah ◽  
Mansoor Maitah
Keyword(s):  
Time Series ◽  
Risk Management ◽  
Time Series Analysis ◽  
Wiener Process ◽  
Stock Price ◽  
Percentage Error ◽  
Portfolio Performance ◽  
Stock Price Prediction ◽  
Series Analysis ◽  
Augmented Dickey Fuller

The attempt to predict stock price movements has occupied investors ever since. Reliable forecasts are a basis for investment management, and improved forecasting results lead to enhanced portfolio performance and sound risk management. While forecasting using the Wiener process has received great attention in the literature, spectral time series analysis has been disregarded in this respect. The paper’s main objective is to evaluate whether spectral time series analysis can produce reliable forecasts of the Aurubis stock price. Aurubis poses a suitable candidate for an investor’s portfolio due to its sound economic and financial situation and the steady dividend policy. Additionally, reliable management contributes to making Aurubis an investment opportunity. To judge if the achieved forecast results can be considered satisfactory, they are compared against the simulation results of a Wiener process. After de-trending the time series using an Augmented Dickey-Fuller test, the residuals were compartmentalized into sine and cosine functions. The frequencies, amplitude, and phase were obtained using the Fast Fourier transform. The mean absolute percentage error measured the accuracy of the stock price prediction, and the results showed that the spectral analysis was able to deliver superior results when comparing the simulation using a Wiener process. Hence, spectral time series can enhance stock price forecasts and consequently improve risk management.

scholarly journals Weak convergence of stochastic integrals with respect to the state occupation measure of a Markov chain

2021 ◽  
Vol 58 (2) ◽  
pp. 372-393
Author(s):  
H. M. Jansen
Keyword(s):  
Markov Chain ◽  
Weak Convergence ◽  
Regime Switching ◽  
Sufficient Conditions ◽  
The State ◽  
Stochastic Integrals ◽  
Occupation Measure ◽  
Generator Matrix ◽  
Markov Modulated ◽  
Erlang Loss

AbstractOur aim is to find sufficient conditions for weak convergence of stochastic integrals with respect to the state occupation measure of a Markov chain. First, we study properties of the state indicator function and the state occupation measure of a Markov chain. In particular, we establish weak convergence of the state occupation measure under a scaling of the generator matrix. Then, relying on the connection between the state occupation measure and the Dynkin martingale, we provide sufficient conditions for weak convergence of stochastic integrals with respect to the state occupation measure. We apply our results to derive diffusion limits for the Markov-modulated Erlang loss model and the regime-switching Cox–Ingersoll–Ross process.

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