Applications of a formula for the variance function of a stochastic process
type: Item
instance of: scholarly article
title: Applications of a formula for the variance function of a stochastic process
zbMATH Open document ID: 0931.60063
DOI: 10.1016/S0167-7152(98)00198-9
published in: Statistics \& Probability Letters
publication date: 2000-02-28T00:00:00Z
review text: The authors consider \(X_t\) solving the following usual one-dimensional stochastic differential equation: \(dX_t= \beta(t,X_t) dB_t+ dN_t\), with \(N_t\) being an adapted square-integrable process with jumps. Itô's formula implies that the variance of \(X_t\) satisfies \[ d\text{ Var}(X_t)= \mathbb{E}[\beta^2(t, X_t)] dt+ \mathbb{E}(\Delta N^2_t)+ 2\text{ Cov}(X_t, d\mathbb{E}(N_t)). \] Comments are done upon some simple particular cases.
Mathematics Subject Classification ID: 60J25
Mathematics Subject Classification ID: 60J60
zbMATH DE Number: 1310362
zbMATH Keywords: stochastic process
zbMATH Keywords: Itô's formula
zbMATH Keywords: variance
author: Ruzong Fan
author: Kenneth Lange
author: Edsel A. Peña
reviewed by: Jacques Franchi
MaRDI profile type: Publication
cites work: Q4844501
cites work: Q4302520
cites work: Q3992729
cites work: Q3774629
cites work: Q4076577
cites work: Q3736771
cites work: Q5185817
cites work: Stochastic differential equations. An introduction with applications.
cites work: Q3997782
full work available at URL: s0167-7152(98)00198-9
OpenAlex ID: W2076719471
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description: scientific article; zbMATH DE number 1310362