scholarly journals Stochastic Volatility Effects on Correlated Log-Normal Random Variables

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Yong-Ki Ma
Keyword(s):  
Stochastic Process ◽  
Density Function ◽  
Process Model ◽  
Numerical Study ◽  
Correction Term ◽  
Order Term ◽  
Splitting Method ◽  
Transition Density ◽  
Analytic Approximation ◽  
Transition Density Function

The transition density function plays an important role in understanding and explaining the dynamics of the stochastic process. In this paper, we incorporate an ergodic process displaying fast moving fluctuation into constant volatility models to express volatility clustering over time. We obtain an analytic approximation of the transition density function under our stochastic process model. Using perturbation theory based on Lie–Trotter operator splitting method, we compute the leading-order term and the first-order correction term and then present the left and right skew scenarios through numerical study.

scholarly journals A Class of Solutions for the Hybrid Kinetic Model in the Tumor-Immune System Competition

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Carlo Cattani ◽  
Armando Ciancio
Keyword(s):  
Immune System ◽  
Kinetic Model ◽  
Density Function ◽  
Hybrid System ◽  
Kinetic Models ◽  
State Transition ◽  
Transition Density ◽  
Realistic Model ◽  
Transition Density Function ◽  
Competing Populations

In this paper, the hybrid kinetic models of tumor-immune system competition are studied under the assumption of pure competition. The solution of the coupled hybrid system depends on the symmetry of the state transition density which characterizes the probability of successful occurrences. Thus by defining a proper transition density function, the solutions of the hybrid system are explicitly computed and applied to a classical (realistic) model of competing populations.

scholarly journals The Sum and Difference of Two Lognormal Random Variables

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
C. F. Lo
Keyword(s):  
Stochastic Process ◽  
Probability Distributions ◽  
Operator Splitting ◽  
Splitting Method ◽  
Unified Approach ◽  
New Approach ◽  
Numerical Examples ◽  
Operator Splitting Method ◽  
Approximate Probability ◽  
Analytical Series

We have presented a new unified approach to model the dynamics of both the sum and difference of two correlated lognormal stochastic variables. By the Lie-Trotter operator splitting method, both the sum and difference are shown to follow a shifted lognormal stochastic process, and approximate probability distributions are determined in closed form. Illustrative numerical examples are presented to demonstrate the validity and accuracy of these approximate distributions. In terms of the approximate probability distributions, we have also obtained an analytical series expansion of the exact solutions, which can allow us to improve the approximation in a systematic manner. Moreover, we believe that this new approach can be extended to study both (1) the algebraic sum ofNlognormals, and (2) the sum and difference of other correlated stochastic processes, for example, two correlated CEV processes, two correlated CIR processes, and two correlated lognormal processes with mean-reversion.

scholarly journals Stochastic process model for solute transport and the associated transport equation

2012 ◽  
Vol 36 (4) ◽  
pp. 1796-1805 ◽  
Author(s):  
Hidekazu Yoshioka ◽  
Koichi Unami ◽  
Toshihiko Kawachi
Keyword(s):  
Stochastic Process ◽  
Solute Transport ◽  
Transport Equation ◽  
Process Model

scholarly journals Stochastic Diffusion Process Based on Generalized Brody Curve: Application to Real Data

2021 ◽  
Vol 2 (1) ◽  
pp. 01-11
Author(s):  
Ahmed Nafidi ◽  
Oussama Rida ◽  
Boujemaa Achchab
Keyword(s):  
Diffusion Process ◽  
Transition Density ◽  
Real Data ◽  
Parameters Estimation ◽  
Likelihood Method ◽  
Stochastic Diffusion ◽  
Life Expectancy At Birth ◽  
Transition Density Function ◽  
Lognormal Diffusion Process ◽  
Trend Functions

A new stochastic diffusion process based on Generalized Brody curve is proposed. Such a process can be considered as an extension of the nonhomogeneous lognormal diffusion process. From the corresponding Itô’s stochastic differential equation (SDE), firstly we establish the probabilistic characteristics of the studied process, such as the solution to the SDE, the probability transition density function and their distribution, the moments function, in particular the conditional and non-conditional trend functions. Secondly, we treat the parameters estimation problem by using the maximum likelihood method in basis of the discrete sampling, thus we obtain nonlinear equations that can be solved by metaheuristic optimization algorithms such as simulated annealing and variable search neighborhood. Finally, we perform a simulation studies and we apply the model to the data of life expectancy at birth in Morocco.

Sign in / Sign up

Export Citation Format

Share Document