The Stochastic Dynamic Exponential and Geometric Brownian Motion on Isolated Time Scales
نویسنده
چکیده
The mathematics of time scales has recently received much attention and holds great promise in a number of areas. In this paper we propose a new area of mathematics, namely the theory of stochastic dynamic equations, which unifies the theories of stochastic differential and difference equations. We give an example involving stochastic dynamic equations, namely an equation modeling a stock price. AMS Subject Classification: 60J65, 26E70, 60G05, 65C30, 39A50.
منابع مشابه
On time-dependent neutral stochastic evolution equations with a fractional Brownian motion and infinite delays
In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory
متن کاملExistence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion
متن کامل
Exponential functionals of Brownian motion, I: Probability laws at fixed time
This paper is the first part of our survey on various results about the distribution of exponential type Brownian functionals defined as an integral over time of geometric Brownian motion. Several related topics are also mentioned.
متن کاملSimulating Exchange Rate Volatility in Iran Using Stochastic Differential Equations
The main purpose of this paper is to analyze the exchange rate volatility in Iran in the time period between 2011/11/27 and 2017/02/25 on a daily basis. As a tradable asset and as an important and effective economic variable, exchange rate plays a decisive role in the economy of a country. In a successful economic management, the modeling and prediction of the exchange rate volatility is esse...
متن کاملExact solutions for Fokker-Plank equation of geometric Brownian motion with Lie point symmetries
In this paper Lie symmetry analysis is applied to find new solution for Fokker Plank equation of geometric Brownian motion. This analysis classifies the solution format of the Fokker Plank equation.
متن کامل