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

Hiroshi Takahashi; Shuya Kanagawa; Ken Ichi Yoshihara

doi:10.1080/07362994.2015.1038840

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

Hiroshi Takahashi, Shuya Kanagawa, Ken Ichi Yoshihara

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

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.

Original language	English
Pages (from-to)	740-755
Number of pages	16
Journal	Stochastic Analysis and Applications
Volume	33
Issue number	4
DOIs	https://doi.org/10.1080/07362994.2015.1038840
Publication status	Published - 2015 Jul 4
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

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10.1080/07362994.2015.1038840

Cite this

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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 = "Black-Scholes type stochastic differential equation, Difference equation, Euler-Maruyama scheme, Weakly dependent random variables",

author = "Hiroshi Takahashi and Shuya Kanagawa and Yoshihara, {Ken Ichi}",

note = "Funding Information: The research is supported by JSPS KAKENHI Grant number 25400211 and 26800063. Publisher Copyright: {\textcopyright} 2015, Taylor & Francis Group, LLC.",

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AU - Takahashi, Hiroshi

AU - Kanagawa, Shuya

AU - Yoshihara, Ken Ichi

PY - 2015/7/4

Y1 - 2015/7/4

N2 - 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.

AB - 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.

KW - Black-Scholes type stochastic differential equation

KW - Difference equation

KW - Euler-Maruyama scheme

KW - Weakly dependent random variables

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

Abstract

Keywords

ASJC Scopus subject areas

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