Analytic functionals of Wiener process and absolute continuity

1982 ◽  
pp. 1-46 ◽  
Author(s):  
Shigeo Kusuoka
Keyword(s):  
Wiener Process ◽  
Absolute Continuity ◽  
Analytic Functionals

ON FINITE ABSOLUTE CONTINUITY OF MEASURES RELATED TO WIENER MEASURE

2009 ◽  
Vol 12 (02) ◽  
pp. 341-352
Author(s):  
G. V. RIABOV
Keyword(s):  
Wiener Process ◽  
General Condition ◽  
Absolute Continuity ◽  
Wiener Measure ◽  
Conditional Distributions ◽  
Disintegration Of Measures

In this paper we study finite absolute continuity with respect to Wiener measure. A general condition of finite absolute continuity in terms of disintegration of measures is given. Finite absolute continuity of Itô processes and conditional distributions of the Wiener process is studied.

scholarly journals A Version of Fundamental Theorem for the Ito-McShane Integral of an Operator-Valued Stochastic Process

2019 ◽  
Vol 12 (1) ◽  
pp. 101-117
Author(s):  
Jeffer Dave Cagubcob ◽  
Mhelmar Avila Labendia
Keyword(s):  
Stochastic Process ◽  
Hilbert Space ◽  
Wiener Process ◽  
Absolute Continuity ◽  
Fundamental Theorem ◽  
Mcshane Integral ◽  
Descriptive Definition

In this paper, we formulate a descriptive definition or a version of fundamental theorem for the Ito-McShane integral of an operator-valued stochastic process with respect to a Hilbert space-valued Wiener process. For this reason, we introduce the concept of belated Mcshane dierentiability and a version of absolute continuity of a Hilbert space-valued stochastic process.

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.

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