an:06661756
Zbl 1351.60079
Damian, Virgil; Ijacu, Daniela
Stochastic flows associated with Stratonovich curve-line integrals
EN
Random Oper. Stoch. Equ. 24, No. 4, 215-223 (2016).
00361202
2016
j
60H15
Stratonovich curve-line integral equations; gradient systems; curve-line stochastic equations
Summary: In this paper, Stratonovich curve-line integrals are used to describe the evolution of a stochastic flow driven by some noncommuting vector fields and independent double Wiener processes. In fact, we analyze the corresponding stochastic evolution of a stochastic flow driven by noncommuting vector fields \({\{g_{1},\dots,g_{m}\}}\) and independent double Wiener processes
\[
\{ W^{i}(t)=(W_{1}^{i}(t_{1}),W_{2}^{i}(t_{2}))\in\mathbb{R}^{2}:t=(t_{1},t_{2})\in D\},\; 1\leq i\leq m.
\]
It is a significant generalization of the case \({m=1}\), considered in a joint work of \textit{V. Damian} and \textit{C. V??rsan} [Math. Rep., Buchar. 14(64), No. 4, 325--332 (2012; Zbl 1289.60114)]. This paper contains two open problems; a good start for a future research.
Zbl 1289.60114