On the rate of convergence of some functionals of a stochastic process

1990 ◽  
Vol 27 (4) ◽  
pp. 805-814 ◽  
Author(s):  
S. Rachev ◽  
P. Todorovic
Keyword(s):  
Stochastic Process ◽  
Soil Erosion ◽  
Rate Of Convergence ◽  
Crop Production ◽  
Limit Theorems ◽  
Infinitely Divisible ◽  
Total Crop ◽  
Infinitely Divisible Processes

This paper is concerned with the rate of convergence of certain functionals associated with a stochastic process arising in the modelling of soil erosion. Some limit theorems are derived for the total crop production Sn over a number n of years, and the rate of convergence of Sn to its limit S is discussed. Some stability assumptions are considered, and particular stable geometric infinitely divisible processes analyzed.

On the rate of convergence of some functionals of a stochastic process

1990 ◽  
Vol 27 (04) ◽  
pp. 805-814 ◽  
Author(s):  
S. Rachev ◽  
P. Todorovic
Keyword(s):  
Stochastic Process ◽  
Soil Erosion ◽  
Rate Of Convergence ◽  
Crop Production ◽  
Limit Theorems ◽  
Infinitely Divisible ◽  
Total Crop ◽  
Infinitely Divisible Processes

This paper is concerned with the rate of convergence of certain functionals associated with a stochastic process arising in the modelling of soil erosion. Some limit theorems are derived for the total crop production Sn over a number n of years, and the rate of convergence of Sn to its limit S is discussed. Some stability assumptions are considered, and particular stable geometric infinitely divisible processes analyzed.

scholarly journals Central and Local Limit Theorems for Numbers of the Tribonacci Triangle

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 880
Author(s):  
Igoris Belovas
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Normal Distribution ◽  
Rate Of Convergence ◽  
Limit Theorems ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Constructive Proof ◽  
The Central Limit Theorem ◽  
Local Limit Theorems

In this research, we continue studying limit theorems for combinatorial numbers satisfying a class of triangular arrays. Using the general results of Hwang and Bender, we obtain a constructive proof of the central limit theorem, specifying the rate of convergence to the limiting (normal) distribution, as well as a new proof of the local limit theorem for the numbers of the tribonacci triangle.

scholarly journals Self-exciting multifractional processes

2021 ◽  
Vol 58 (1) ◽  
pp. 22-41
Author(s):  
Fabian A. Harang ◽  
Marc Lagunas-Merino ◽  
Salvador Ortiz-Latorre
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
Rate Of Convergence ◽  
Existence And Uniqueness ◽  
Volterra Equation ◽  
The Self ◽  
The Past ◽  
Stochastic Volterra Equation ◽  
Multifractional Brownian Motion ◽  
Self Organizing

AbstractWe propose a new multifractional stochastic process which allows for self-exciting behavior, similar to what can be seen for example in earthquakes and other self-organizing phenomena. The process can be seen as an extension of a multifractional Brownian motion, where the Hurst function is dependent on the past of the process. We define this by means of a stochastic Volterra equation, and we prove existence and uniqueness of this equation, as well as giving bounds on the p-order moments, for all $p\geq1$. We show convergence of an Euler–Maruyama scheme for the process, and also give the rate of convergence, which is dependent on the self-exciting dynamics of the process. Moreover, we discuss various applications of this process, and give examples of different functions to model self-exciting behavior.

scholarly journals Prioritization of Sub-Watersheds to Sediment Yield and Evaluation of Best Management Practices in Highland Ethiopia, Finchaa Catchment

Land ◽  
2021 ◽  
Vol 10 (6) ◽  
pp. 650
Author(s):  
Wakjira Takala Dibaba ◽  
Tamene Adugna Demissie ◽  
Konrad Miegel
Keyword(s):  
Soil Erosion ◽  
Best Management Practices ◽  
Sediment Yield ◽  
Soil Loss ◽  
Crop Production ◽  
Management Practices ◽  
Assessment Tool ◽  
Swat Model ◽  
Sediment Yields ◽  
Soil And Water

Excessive soil loss and sediment yield in the highlands of Ethiopia are the primary factors that accelerate the decline of land productivity, water resources, operation and function of existing water infrastructure, as well as soil and water management practices. This study was conducted at Finchaa catchment in the Upper Blue Nile basin of Ethiopia to estimate the rate of soil erosion and sediment loss and prioritize the most sensitive sub-watersheds using the Soil and Water Assessment Tool (SWAT) model. The SWAT model was calibrated and validated using the observed streamflow and sediment data. The average annual sediment yield (SY) in Finchaa catchment for the period 1990–2015 was 36.47 ton ha−1 yr−1 with the annual yield varying from negligible to about 107.2 ton ha−1 yr−1. Five sub-basins which account for about 24.83% of the area were predicted to suffer severely from soil erosion risks, with SY in excess of 50 ton ha−1 yr−1. Only 15.05% of the area within the tolerable rate of loss (below 11 ton ha−1yr−1) was considered as the least prioritized areas for maintenance of crop production. Despite the reasonable reduction of sediment yields by the management scenarios, the reduction by contour farming, slope terracing, zero free grazing and reforestation were still above the tolerable soil loss. Vegetative contour strips and soil bund were significant in reducing SY below the tolerable soil loss, which is equivalent to 63.9% and 64.8% reduction, respectively. In general, effective and sustainable soil erosion management requires not only prioritizations of the erosion hotspots but also prioritizations of the most effective management practices. We believe that the results provided new and updated insights that enable a proactive approach to preserve the soil and reduce land degradation risks that could allow resource regeneration.

Central Limit Theorems for Interchangeable Processes

1958 ◽  
Vol 10 ◽  
pp. 222-229 ◽  
Author(s):  
J. R. Blum ◽  
H. Chernoff ◽  
M. Rosenblatt ◽  
H. Teicher
Keyword(s):  
Stochastic Process ◽  
Probability Measure ◽  
Central Limit ◽  
Joint Distribution ◽  
Limit Theorems ◽  
Random Variables ◽  
Central Limit Theorems ◽  
Probability Measures ◽  
Image Position ◽  
Positive Integers

Let {Xn} (n = 1, 2 , …) be a stochastic process. The random variables comprising it or the process itself will be said to be interchangeable if, for any choice of distinct positive integers i 1, i 2, H 3 … , ik, the joint distribution of depends merely on k and is independent of the integers i 1, i 2, … , i k. It was shown by De Finetti (3) that the probability measure for any interchangeable process is a mixture of probability measures of processes each consisting of independent and identically distributed random variables.

scholarly journals Non-central limit theorems for functionals of random fields on hypersurfaces

2020 ◽  
Vol 24 ◽  
pp. 315-340
Author(s):  
Andriy Olenko ◽  
Volodymyr Vaskovych
Keyword(s):  
Rate Of Convergence ◽  
Central Limit ◽  
Random Fields ◽  
Limit Theorems ◽  
Gaussian Random Fields ◽  
Central Limit Theorems ◽  
Integral Functionals ◽  
Asymptotic Results ◽  
Non Linear ◽  
Linear Integral

This paper derives non-central asymptotic results for non-linear integral functionals of homogeneous isotropic Gaussian random fields defined on hypersurfaces in ℝd. We obtain the rate of convergence for these functionals. The results extend recent findings for solid figures. We apply the obtained results to the case of sojourn measures and demonstrate different limit situations.

scholarly journals Sediment Yield and Soil Loss Estimation Using GIS Based Soil Erosion Model: A Case Study in the MAN Catchment, Madhya Pradesh, India

2021 ◽  
Vol 8 (1) ◽  
pp. 26
Author(s):  
Manti Patil ◽  
Radheshyam Patel ◽  
Arnab Saha
Keyword(s):  
Spatial Distribution ◽  
Soil Erosion ◽  
Soil Loss ◽  
Crop Production ◽  
Erosion Rate ◽  
Agricultural Land ◽  
Reservoir Sedimentation ◽  
Reservoir Water ◽  
Slope Length ◽  
Soil Erosion Rate

Soil erosion is one of the most critical environmental hazards of recent times. It broadly affects to agricultural land and reservoir sedimentation and its consequences are very harmful. In agricultural land, soil erosion affects the fertility of soil and its composition, crop production, soil quality and land quality, yield and crop quality, infiltration rate and water holding capacity, organic matter and plant nutrient and groundwater regimes. In reservoir sedimentation process the consequences of soil erosion process are reduction of the reservoir capacity, life of reservoir, water supply, power generation etc. Based on these two aspects, an attempt has been made to the present study utilizing Revised Universal Soil Loss Equation (RUSLE) has been used in integration with remote sensing and GIS techniques to assess the spatial pattern of annual rate of soil erosion, average annual soil erosion rate and erosion prone areas in the MAN catchment. The RUSLE considers several factors such as rainfall, soil erodibility, slope length and steepness, land use and land cover and erosion control practice for soil erosion prediction. In the present study, it is found that average annual soil erosion rate for the MAN catchment is 13.01-tons/ha/year, which is higher than that of adopted and recommended values for the project. It has been found that 53% area of the MAN catchment has negligible soil erosion rate (less than 2-tons/ha/year). Its spatial distribution found on flat land of upper MAN catchment. It has been detected that 26% area of MAN catchment has moderate to extremely severe soil erosion rate (greater than 10-tons/ha/year). Its spatial distribution has been found on undulated topography of the middle MAN catchment. It is proposed to treat this area by catchment area treatment activity.

Sign in / Sign up

Export Citation Format

Share Document