A formula for transition density function under Girsanov transform

2007 ◽  
Vol 77 (6) ◽  
pp. 658-666 ◽  
Author(s):  
Ruili Song ◽  
Jiangang Ying
Keyword(s):  
Density Function ◽  
Transition Density ◽  
Transition Density Function ◽  
Girsanov Transform

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 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.

A diffusion model for fatigue crack growth

1979 ◽  
Vol 367 (1728) ◽  
pp. 47-58 ◽  
Keyword(s):  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Diffusion Equation ◽  
Stochastic Model ◽  
Crack Growth ◽  
Diffusion Model ◽  
Critical Size ◽  
Transition Density ◽  
Transition Density Function ◽  
Drift Parameter

A stochastic model is proposed for the propagation of a fatigue crack. It is shown that fatigue crack growth can be described by a transition density function, and that the probability of a fatigue crack reaching a critical size can be determined by solving the diffusion equation. The commonly used rate of crack growth, d a /d N , appears in the diffusion model as the drift parameter.

Optimal control of a finite dam: Wiener process input

1987 ◽  
Vol 24 (1) ◽  
pp. 186-199 ◽  
Author(s):  
Lam Yeh ◽  
Lou Jiann Hua
Keyword(s):  
Optimal Control ◽  
Wiener Process ◽  
Optimal Policy ◽  
Average Cost ◽  
Transition Density ◽  
Discounted Cost ◽  
Transition Density Function ◽  
Long Run ◽  
The Resolvent Operator ◽  
Finite Dam

The problem of optimal control of a finite dam in the class of policies has been considered by Lam Yeh [6], [7]. In this paper, by using the first Dynkin formula, the same problems of specifying an optimal policy in the class of the policies to minimize the expected total discounted cost as well as the long-run average cost are considered. Both the expected total discounted cost and long-run average cost are determined explicitly, and then the optimal policy can be found numerically, Also, we obtain the transition density function and the resolvent operator of a reflecting Wiener process.

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