Asymptotic Behavior of Solutions of Some Difference Equations Defined by Weakly Dependent Random Vectors

Abstract

In this article, we consider not only stochastic differential equations driven by the Wiener process but also by processes with stationary increments from the view points of time series analysis for mathematical finance. Corresponding to Black-Scholes type stochastic differential equations, we consider difference equations defined by weakly dependent sequence of random vectors and examine the asymptotic behavior of their solutions.

Keywords:

• Difference equation
• Weakly dependent random variables
• Euler-Maruyama scheme
• Black-Scholes type stochastic differential equation

Mathematical Subject Classification:

• 39A50
• 39A30
• 60G10
• 60H10