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 |
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Pages (from-to) | 21-47 |
Journal | Stochastic Processes and their Applications |
Volume | 68 |
DOIs | |
Publication status | Published - 30 May 1997 |
Keywords
- Girsanov transformations
- Markov fields
- Non-causal stochastic calculus
- Stochastic differential equations