Existence and uniqueness theorems for fBm stochastic differential equations
type: Item
instance of: scholarly article
title: Existence and uniqueness theorems for fBm stochastic differential equations
zbMATH Open document ID: 0924.60042
author: Vo V. Anh
author: Marina Kleptsyna
author: Peter E. Kloeden
published in: Problems of Information Transmission
publication date: 1999-11-14T00:00:00Z
review text: Conditions are identified and then proofs are given that establish existence and uniqueness of the solution of stochastic ordinary differential equations of the following two forms: \[ dX_t= a(t,X_t)dt+ b(t,X_t)dB_t^h, \qquad X_0=x, \tag{1} \] where \(B_t^h\) is a scalar fractional Brownian motion with Hurst index \(h\) between \(\frac 12\) and 1, \[ dX_t= a(t,X_t)dt+ dB_t^h, \qquad X_0=x, \tag{2} \] where \(B_t^h\) is a \(d\)-dimensional vector fractional Brownian motion with Hurst index \(h\) between \(\frac 12\) and 1.
reviewed by: Melvin D. Lax
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 1294990
zbMATH Keywords: stochastic ordinary differential equations
zbMATH Keywords: fractional Brownian motion
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1294990