O. Tymoshenko

Markov property for systems driven by the Brownian sheet

We study stochastic systems driven by a Brownian sheet and formulate a Markov property adapted to their two-parameter structure. For time-space homogeneous It\^o sheets, the future evolution from a point $(t,x)$ is not determined by the single value $Y(t,x)$ alone, but also by the boundary data along the horizontal and...