Second order stochastic differential equations with Dirichlet boundary conditions

David Nualart and Etienne Pardoux

Stochastic Processes and their Applications, 1991, vol. 39, issue 1, 1-24

Abstract: 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.

Keywords: stochastic; differential; equations; Markov; processes; noncausal; stochastic; calculus; Skorohod; and; Stratonovich; stochastic; integrals; anticipating; Girsanov; transformation (search for similar items in EconPapers)
Date: 1991
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Citations: View citations in EconPapers (3)

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