Second order stochastic differential equations with Dirichlet boundary conditions

We consider the second order stochastic differential equation 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(1) = b. We show pathwise existence and uniqueness of a solution assuming some smoothness and monotonicity conditions on f, and we study the Markov property of the solution using an extended version of the Girsanov theorem due to Kusuoka.

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Year of publication:	1991
Authors:	Nualart, David ; Pardoux, Etienne
Published in:	Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 39.1991, 1, p. 1-24
Publisher:	Elsevier
Keywords:	stochastic differential equations Markov processes noncausal stochastic calculus Skorohod and Stratonovich stochastic integrals anticipating Girsanov transformation

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10008875748