Two-parameter diffusion processes and martingales

D. Nualart

Stochastic Processes and their Applications, 1983, vol. 15, issue 1, 31-57

Abstract: We introduce a class of two-parameter processes which are diffusions on each coordinate and satisfy a particular Markov property related to the partial ordering in R2+. These processes can be expressed as solutions of some stochastic integral equations driven by a two-parameter Wiener process and two families of ordinary Brownian motions. This result is based on a characterization of two-parameter martingales with orthogonal increments.

Date: 1983
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