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Stochastic flows associated with Stratonovich curve-line integrals. (English) Zbl 1351.60079
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 V. Damian and C. Vârsan [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.
MSC:
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
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