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Boundary Value Problems for Stochastic Differential Equations

Nualart, David
; 
Pardoux, E.
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Abstract
In this paper, we study stochastic differential equations with boundary conditions at the endpoints of a time interval (instead of the customary initial condition). We present existence and uniqueness results and study the Markov property of the solution. In the one-dimensional case, we prove that the solution is a Markov field iff the drift is affine.
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This is the published version, also available here: http://dx.doi.org/10.1214/aop/1176990337.
Date
1991
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Institute of Mathematical Statistics (IMS)
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Mathematics Scholarly Works
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NualartD_AP_19(3)1118.pdf
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Keywords
Stochastic differential equations, equations with boundary conditions, Markov processes, Markov fields
Citation
Nualart, D.; Pardoux, E. Boundary Value Problems for Stochastic Differential Equations. Ann. Probab. 19 (1991), no. 3, 1118--1144. http://dx.doi.org/10.1214/aop/1176990337.
URI
https://hdl.handle.net/1808/17060
DOI
10.1214/aop/1176990337
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