Nonlinear stochastic differential equation as the background of financial fluctuations

2009 ◽  
Author(s):  
V. Gontis ◽  
B. Kaulakys ◽  
J. Ruseckas ◽  
Massimo Macucci ◽  
Giovanni Basso
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Financial Fluctuations ◽  
Nonlinear Stochastic Differential Equation

Lévy-type nonlinear stochastic dynamic model, method and analysis

2019 ◽  
Vol 19 (05) ◽  
pp. 1950033
Author(s):  
Gangarm S. Ladde ◽  
Youngsoo Seol
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Dynamic Model ◽  
Existence And Uniqueness ◽  
Type Theorem ◽  
Main Idea ◽  
Stochastic Dynamic ◽  
Innovative Idea ◽  
The One ◽  
Nonlinear Stochastic Differential Equation

In this work, we consider a prototype stochastic dynamic model for dynamic processes in biological, chemical, economic, financial, medical, military, physical and technological sciences. The dynamic model is described by Lévy-type nonlinear stochastic differential equation. The model validation is established by the usage of Lyapunov-like function. The basic innovative idea is to transform a nonlinear Lévy-type nonlinear stochastic differential into a simpler stochastic differential equation that is easily tested for the existence and uniqueness theorem. Using the nature of Lyapunov-like function, the existence and uniqueness of solution of the original Lévy-type nonlinear stochastic differential equation is established. The main idea of the proof is based on the property of the one-to-one and onto transformation. As the byproduct of the analysis, it is shown that the closed-form implicit solution of transformed stochastic differential equation is a positive martingale. Furthermore, using the change of measure, a Girsanov-type theorem for Lévy-type nonlinear stochastic dynamic model is established.

scholarly journals Ice Gouge Depth Determination Via an Efficient Stochastic Dynamics Technique

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Nikolaos Gazis ◽  
Ioannis A. Kougioumtzoglou ◽  
Edoardo Patelli
Keyword(s):  
Differential Equation ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Stochastic Differential Equation ◽  
Path Integral ◽  
Stochastic Dynamics ◽  
Simplified Model ◽  
Preliminary Design ◽  
Depth Determination ◽  
Nonlinear Stochastic Differential Equation

A simplified model of the motion of a grounding iceberg for determining the gouge depth into the seabed is proposed. Specifically, taking into account uncertainties relating to the soil strength, a nonlinear stochastic differential equation governing the evolution of the gouge length/depth in time is derived. Further, a recently developed Wiener path integral (WPI) based approach for solving approximately the nonlinear stochastic differential equation is employed; thus, circumventing computationally demanding Monte Carlo based simulations and rendering the approach potentially useful for preliminary design applications. The accuracy/reliability of the approach is demonstrated via comparisons with pertinent Monte Carlo simulation (MCS) data.

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