A second-order Stratonovich differential equation with boundary conditions

Aureli Alabert; David Nualart

doi:https://doi.org/10.1016/S0304-4149(97)00021-5

A second-order Stratonovich differential equation with boundary conditions

Aureli Alabert, David Nualart

Department of Mathematics

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

2 Citations (Scopus)

Abstract

In this paper we show that the solution of a second-order stochastic differential equation with diffusion coefficient σẊt and boundary conditions X0 = 0 and X1 = 1 is a 2-Markov field if and only if the drift is a linear function. The proof is based on the method of change of probability and makes use of the techniques of Malliavin calculus.

Original language	English
Pages (from-to)	21-47
Journal	Stochastic Processes and their Applications
Volume	68
DOIs	https://doi.org/10.1016/S0304-4149(97)00021-5
Publication status	Published - 30 May 1997

Keywords

Girsanov transformations
Markov fields
Non-causal stochastic calculus
Stochastic differential equations

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title = "A second-order Stratonovich differential equation with boundary conditions",

abstract = "In this paper we show that the solution of a second-order stochastic differential equation with diffusion coefficient σẊt and boundary conditions X0 = 0 and X1 = 1 is a 2-Markov field if and only if the drift is a linear function. The proof is based on the method of change of probability and makes use of the techniques of Malliavin calculus.",

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T1 - A second-order Stratonovich differential equation with boundary conditions

AU - Alabert, Aureli

AU - Nualart, David

PY - 1997/5/30

Y1 - 1997/5/30

N2 - In this paper we show that the solution of a second-order stochastic differential equation with diffusion coefficient σẊt and boundary conditions X0 = 0 and X1 = 1 is a 2-Markov field if and only if the drift is a linear function. The proof is based on the method of change of probability and makes use of the techniques of Malliavin calculus.

AB - In this paper we show that the solution of a second-order stochastic differential equation with diffusion coefficient σẊt and boundary conditions X0 = 0 and X1 = 1 is a 2-Markov field if and only if the drift is a linear function. The proof is based on the method of change of probability and makes use of the techniques of Malliavin calculus.

KW - Girsanov transformations

KW - Markov fields

KW - Non-causal stochastic calculus

KW - Stochastic differential equations

U2 - https://doi.org/10.1016/S0304-4149(97)00021-5

DO - https://doi.org/10.1016/S0304-4149(97)00021-5

M3 - Article

VL - 68

SP - 21

EP - 47

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

SN - 0304-4149

ER -