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Second order stochastic differential equations with Dirichlet boundary conditions
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Abstract
We consider the second order stochastic differential equation Xt + f(Xt, Xt) =
Wt where t runs on the interval [0, 1], {Wt} is an ordinary Brownian motion and we impose
the Dirichlet boundary conditions X(0) = a and X(l) = b. We show pathwise existence
and uniqueness of a solution assuming sorne smoothness and monotonicity conditions on
f, and we study the Markov property of the solution using an extended version of the
Girsanov theorem dueto Kusuoka.
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Preprint enviat per a la seva publicació en una revista científica: Stochastic Processes and their Applications. Volume 39, Issue 1, October 1991, Pages 1-24. [https://doi.org/10.1016/0304-4149(91)90028-B]
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NUALART, David and PARDOUX, Etienne. Second order stochastic differential equations with Dirichlet boundary conditions. [consulted: 6 of June of 2026]. Available at: https://hdl.handle.net/2445/151847