A second-order Stratonovich differential equation with boundary conditions
type: Item
instance of: scholarly article
title: A second-order Stratonovich differential equation with boundary conditions
zbMATH Open document ID: 0890.60052
DOI: 10.1016/S0304-4149(97)00021-5
published in: Stochastic Processes and their Applications
publication date: 1998-03-29T00:00:00Z
review text: The second-order SDE of the form \[ \ddot X_t= f(X_t)+ \sigma \dot X_t \circ \dot W_t,\qquad 0\leq t\leq 1, \] with boundary conditions \(X_0=0\), \(X_1=1\) is studied where \(W_t\) is a standard Wiener process, \(\sigma >0\) is a constant, and \(f:R\to R\) is a continuous function. Because of the terminal condition on \(X\), the solution is not expected to be a process adapted with respect to the Wiener process \(W_t\). Using the techniques of Malliavin calculus and the method of change of probability, the authors tackle the problem of existence and uniqueness of solutions and they show that the solution is a 2-Markov field if and only if the drift \(f\) is an affine function.
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60H07
zbMATH DE Number: 1134833
zbMATH Keywords: stochastic differential equations
zbMATH Keywords: Markov fields
zbMATH Keywords: non-casual stochastic calculus
Wikidata QID: Q115339243
author: Aureli Alabert
author: David Nualart
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1134833