Inverse Gaussian distributed method of moments for agglomerate coagulation due to Brownian motion in the entire size regime

2021 ◽  
Vol 173 ◽  
pp. 121229
Author(s):  
H. Jiang ◽  
M. Yu ◽  
J. Shen ◽  
M. Xie
Keyword(s):  
Brownian Motion ◽  
Method Of Moments ◽  
Inverse Gaussian ◽  
Size Regime ◽  
Distributed Method

scholarly journals Second-order limit laws for occupation times of fractional Brownian motion

2017 ◽  
Vol 54 (2) ◽  
pp. 444-461 ◽  
Author(s):  
Fangjun Xu
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Method Of Moments ◽  
Second Order ◽  
Hurst Index ◽  
Occupation Times ◽  
Limit Laws ◽  
Additive Functionals ◽  
Finite Dimensional ◽  
Functional Version

Abstract We prove a second-order limit law for additive functionals of a d-dimensional fractional Brownian motion with Hurst index H = 1 / d, using the method of moments and extending the Kallianpur–Robbins law, and then give a functional version of this result. That is, we generalize it to the convergence of the finite-dimensional distributions for corresponding stochastic processes.

CALIBRATING THE SMILE WITH MULTIVARIATE TIME-CHANGED BROWNIAN MOTION AND THE ESSCHER TRANSFORM

2014 ◽  
Vol 17 (04) ◽  
pp. 1450023 ◽  
Author(s):  
GIAN LUCA TASSINARI ◽  
MICHELE LEONARDO BIANCHI
Keyword(s):  
Time Series ◽  
Brownian Motion ◽  
Correlation Matrix ◽  
Asset Returns ◽  
Inverse Gaussian ◽  
Esscher Transform ◽  
Pricing Models ◽  
Simple Correlation ◽  
Complex Dependence ◽  
Normal Inverse Gaussian

In this study, we investigate two multivariate time-changed Brownian motion option pricing models in which the connection between the historical measure P and the risk-neutral measure Q is given by the Esscher transform. The models incorporate skewness, kurtosis and more complex dependence structures among stocks log-returns than the simple correlation matrix. The two models can be seen as a multivariate extension of the normal inverse Gaussian (NIG) model and the variance gamma (VG) model, respectively. We discuss two possible approaches to estimate historical asset returns and calibrate univariate option implied volatilities. While the first approach considers only time series of log-returns, the second approach makes use of both time series of log-returns and univariate observed volatility surfaces. To calibrate the models, there is no need of liquid multivariate derivative quotes.

scholarly journals THE NORMAL INVERSE GAUSSIAN DISTRIBUTION AND SPOT PRICE MODELLING IN ENERGY MARKETS

2004 ◽  
Vol 07 (02) ◽  
pp. 177-192 ◽  
Author(s):  
FRED ESPEN BENTH ◽  
JŪRATĖ ŠALTYTĖ-BENTH
Keyword(s):  
Brownian Motion ◽  
Gaussian Distribution ◽  
Market Price ◽  
Energy Markets ◽  
Inverse Gaussian Distribution ◽  
Spot Price ◽  
Inverse Gaussian ◽  
Statistical Point ◽  
Normal Inverse Gaussian Distribution ◽  
Normal Inverse Gaussian

We model spot prices in energy markets with exponential non-Gaussian Ornstein–Uhlenbeck processes. We generalize the classical geometric Brownian motion and Schwartz' mean-reversion model by introducing Lévy processes as the driving noise rather than Brownian motion. Instead of modelling the spot price dynamics as the solution of a stochastic differential equation with jumps, it is advantageous from a statistical point of view to model the price process directly. Imposing the normal inverse Gaussian distribution as the statistical model for the Lévy increments, we obtain a superior fit compared to the Gaussian model when applied to spot price data from the oil and gas markets. We also discuss the problem of pricing forwards and options and outline how to find the market price of risk in an incomplete market.

Description of Atmospheric Aerosol Dynamics Using an Inverse Gaussian Distributed Method of Moments

2020 ◽  
Vol 77 (9) ◽  
pp. 3011-3031
Author(s):  
J. Shen ◽  
M. Yu ◽  
J. Lin
Keyword(s):  
Size Distribution ◽  
Method Of Moments ◽  
Lognormal Distribution ◽  
Atmospheric Aerosol ◽  
Aerosol Size Distribution ◽  
Geometric Standard Deviation ◽  
Test Cases ◽  
Size Distributions ◽  
Inverse Gaussian ◽  
Aerosol Dynamics

Abstract For nearly 60 years, the lognormal distribution has been the most widely used function in the field of atmospheric science for characterizing atmospheric aerosol size distribution. We verify whether the three-parameter inverse Gaussian distribution (IGD) is a more suitable function than the lognormal distribution for characterizing aerosol size distribution. An attractive feature of IGD is that with it a new method of moments (MOM) can be established for resolving atmospheric aerosol dynamics which is described by a kinetic aerosol dynamics equation, i.e., inverse Gaussian distributed MOM (IGDMOM). The advantage of IGDMOM is that all of its moments can be analytically calculated using a closure moment function inherited from IGD. The precision and efficiency of IGDMOM are verified by comparing it with other recognizable methods in test cases of four representative atmospheric aerosol dynamics. Several key statistical quantities determining aerosol size distributions, including kth moments (k = 0, 1/3, 2/3, and 2), geometric standard deviation, skewness, and kurtosis, are evaluated. IGDMOM has higher precision than the lognormal MOM with nearly identical efficiency. The article provides a novel alternative to atmospheric scientists for solving kinetic aerosol dynamics equations.

scholarly journals An Analogue of Pitman’s 2M — X Theorem for Exponential Wiener Functionals Part II: The Role of the Generalized Inverse Gaussian Laws

2001 ◽  
Vol 162 ◽  
pp. 65-86 ◽  
Author(s):  
Hiroyuki Matsumoto ◽  
Marc Yor
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
Diffusion Process ◽  
Generalized Inverse ◽  
Inverse Gaussian ◽  
Brownian Motion With Drift ◽  
Generalized Inverse Gaussian

In Part I of this work, we have shown that the stochastic process Z(µ) defined by (8.1) below is a diffusion process, which may be considered as an extension of Pitman’s 2M — X theorem. In this Part II, we deduce from an identity in law partly due to Dufresne that Z(µ) is intertwined with Brownian motion with drift µ and that the intertwining kernel may be expressed in terms of Generalized Inverse Gaussian laws.

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