PreprintOn linear stochastic flowsBeniamin Goldys and Szymon PeszatAbstractWe study the existence of the stochastic flow associated to a linear stochastic evolution equation \[ \mathrm{d} X= AX\,\mathrm{d} t +\sum_{k} B_k X\,\mathrm{d} W_k, \] on a Hilbert space. Our first result covers the case where \(A\) is the generator of a \(C_0\)semigroup, and \((B_k)\) is a sequence of bounded linear operators such that \(\sum_k\B_k\<+\infty\). We also provide sufficient conditions for the existence of stochastic flows in the Schatten classes beyond the space of HilbertSchmidt operators. Some new results and examples concerning the socalled commutative case are presented as well. Keywords: stochastic flow, stochastic equation with multiplicative noise, Schatten class.AMS Subject Classification: Primary 60H15; secondary 60G15, 60G60.
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