scholarly journals On using convolutions with exponential distributions for solving a Kolmogorov backward equation

2019 ◽  
Vol 1203 ◽  
pp. 012101
Author(s):  
O Kudryavtsev ◽  
V Rodochenko
Keyword(s):  
Exponential Distributions ◽  
Backward Equation

Embedding non-linear filtering in autonomous underwater vehicle dynamics via the Kolmogorov backward equation

2021 ◽  
pp. 014233122110196
Author(s):  
Ravish H. Hirpara ◽  
Shambhu N. Sharma
Keyword(s):  
State Vector ◽  
Autonomous Underwater Vehicle ◽  
Underwater Vehicle ◽  
Linear Filtering ◽  
Homogeneous Markov Process ◽  
Non Linear ◽  
Backward Equation ◽  
Noise Correction ◽  
Ito Process ◽  
Correction Terms

This paper revisits the state vector of an autonomous underwater vehicle (AUV) dynamics coupled with the underwater Markovian stochasticity in the ‘non-linear filtering’ context. The underwater stochasticity is attributed to atmospheric turbulence, planetary interactions, sea surface conditions and astronomical phenomena. In this paper, we adopt the Itô process, a homogeneous Markov process, to describe the AUV state vector evolution equation. This paper accounts for the process noise as well as observation noise correction terms by considering the underwater filtering model. The non-linear filtering of the paper is achieved using the Kolmogorov backward equation and the evolution of the conditional characteristic function. The non-linear filtering equation is the cornerstone formalism of stochastic optimal control systems. Most notably, this paper introduces the non-linear filtering theory into an underwater vehicle stochastic system by constructing a lemma and a theorem for the underwater vehicle stochastic differential equation that were not available in the literature.

scholarly journals Complexity traits and synchrony of cryptocurrencies price dynamics

2021 ◽  
Author(s):  
Davide Provenzano ◽  
Rodolfo Baggio
Keyword(s):  
Time Series ◽  
Complex Network ◽  
Complex Structures ◽  
Slope Parameter ◽  
Exponential Distributions ◽  
Horizontal Visibility ◽  
Time Period ◽  
Before And After ◽  
Visibility Algorithm ◽  
Similar Complex

AbstractIn this study, we characterized the dynamics and analyzed the degree of synchronization of the time series of daily closing prices and volumes in US$ of three cryptocurrencies, Bitcoin, Ethereum, and Litecoin, over the period September 1,2015–March 31, 2020. Time series were first mapped into a complex network by the horizontal visibility algorithm in order to revel the structure of their temporal characters and dynamics. Then, the synchrony of the time series was investigated to determine the possibility that the cryptocurrencies under study co-bubble simultaneously. Findings reveal similar complex structures for the three virtual currencies in terms of number and internal composition of communities. To the aim of our analysis, such result proves that price and volume dynamics of the cryptocurrencies were characterized by cyclical patterns of similar wavelength and amplitude over the time period considered. Yet, the value of the slope parameter associated with the exponential distributions fitted to the data suggests a higher stability and predictability for Bitcoin and Litecoin than for Ethereum. The study of synchrony between the time series investigated displayed a different degree of synchronization between the three cryptocurrencies before and after a collapse event. These results could be of interest for investors who might prefer to switch from one cryptocurrency to another to exploit the potential opportunities of profit generated by the dynamics of price and volumes in the market of virtual currencies.

scholarly journals A Longitudinal Study of the Bladder Cancer Applying a State-Space Model with Non-Exponential Staying Time in States

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 363
Author(s):  
Delia Montoro-Cazorla ◽  
Rafael Pérez-Ocón ◽  
Alicia Pereira das Neves-Yedig
Keyword(s):  
Bladder Cancer ◽  
Longitudinal Study ◽  
State Space Model ◽  
Exponential Distributions ◽  
Significance Level ◽  
Phase Type Distributions ◽  
And Performance ◽  
The Times ◽  
Comparison Of The Results ◽  
Staying Time

A longitudinal study for 847 bladder cancer patients for a period of fifteen years is presented. After the first surgery, the patients undergo successive ones (recurrences). A state-model is selected for analyzing the evolution of the cancer, based on the distribution of the times between recurrences. These times do not follow exponential distributions, and are approximated by phase-type distributions. Under these conditions, a multidimensional Markov process governs the evolution of the disease. The survival probability and mean times in the different states (levels) of the disease are calculated empirically and also by applying the Markov model, the comparison of the results indicate that the model is well-fitted to the data to an acceptable significance level of 0.05. Two sub-cohorts are well-differenced: those reaching progression (the bladder is removed) and those that do not. These two cases are separately studied and performance measures calculated, and the comparison reveals details about the characteristics of the patients in these groups.

Influence of the Distribution of Tail States in a-Si:H on the Field Dependence of Carrier Drift Mobilities

2004 ◽  
Vol 808 ◽  
Author(s):  
Monica Brinza ◽  
Evguenia V. Emelianova ◽  
André Stesmans ◽  
Guy J. Adriaenssens
Keyword(s):  
Field Dependence ◽  
Carrier Mobility ◽  
Transport Model ◽  
Chemical Vapor ◽  
Gaussian Component ◽  
Dispersive Transport ◽  
Exponential Distributions ◽  
Band Tail ◽  
Multiple Trapping ◽  
Gaussian Density

ABSTRACTExponential distributions of tail states have been able, within the framework of a multiple-trapping transport model, to account rather well for the time-of-flight photoconductivity transients that are measured with ‘standard’ a-Si:H, i.e. material prepared by plasma-enhanced chemical vapor deposition at ∼250°C. A field-dependent carrier mobility in the dispersive transport regime is part of the observations. However, samples prepared in an expanding thermal plasma, although still exhibiting the dispersive transients, fail to show this field dependence. The presence of a Gaussian component in the density of valence-band tail states can account for such behavior for the hole transients. Nanoscale ordered inclusions in the amorphous matrix are thought to be responsible for the Gaussian density of states contribution.

scholarly journals Are Special Processes at Work in the Rapid Intensification of Tropical Cyclones?

2015 ◽  
Vol 143 (3) ◽  
pp. 878-882 ◽  
Author(s):  
Roman Kowch ◽  
Kerry Emanuel
Keyword(s):  
Tropical Cyclone ◽  
Tropical Cyclones ◽  
Internal Variability ◽  
Open Ocean ◽  
Rapid Intensification ◽  
Exponential Distributions ◽  
Frequency Distributions ◽  
Fat Tail ◽  
Dissipation Rates ◽  
Special Factors

Abstract Probably not. Frequency distributions of intensification and dissipation developed from synthetic open-ocean tropical cyclone data show no evidence of significant departures from exponential distributions, though there is some evidence for a fat tail of dissipation rates. This suggests that no special factors govern high intensification rates and that tropical cyclone intensification and dissipation are controlled by statistically random environmental and internal variability.

Univariate and bivariate extensions of the generalized exponential distributions

2021 ◽  
Vol 71 (6) ◽  
pp. 1581-1598
Author(s):  
Vahid Nekoukhou ◽  
Ashkan Khalifeh ◽  
Hamid Bidram
Keyword(s):  
Em Algorithm ◽  
Exponential Distribution ◽  
Bivariate Distribution ◽  
Generalized Exponential Distribution ◽  
Exponential Distributions ◽  
Unknown Parameters ◽  
Data Set ◽  
New Class ◽  
Special Cases ◽  
Univariate Distribution

Abstract The main aim of this paper is to introduce a new class of continuous generalized exponential distributions, both for the univariate and bivariate cases. This new class of distributions contains some newly developed distributions as special cases, such as the univariate and also bivariate geometric generalized exponential distribution and the exponential-discrete generalized exponential distribution. Several properties of the proposed univariate and bivariate distributions, and their physical interpretations, are investigated. The univariate distribution has four parameters, whereas the bivariate distribution has five parameters. We propose to use an EM algorithm to estimate the unknown parameters. According to extensive simulation studies, we see that the effectiveness of the proposed algorithm, and the performance is quite satisfactory. A bivariate data set is analyzed and it is observed that the proposed models and the EM algorithm work quite well in practice.

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