Geodesic
Brownian motion with drift in a Hilbert space and its application in integration theory
Teoriâ veroâtnostej i ee primeneniâ, Tome 38 (1993) no. 3, pp. 629-634

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Sufficient conditions are given under which a Brownian motion with drift in a Hilbert space has an invariant measure. We prove that if the measure is differentiable, then its logarithmic gradient is equal to the drift coefficient. The results obtained constitute a basis for the reconstruction of a differentiable measure from its logarithmic derivatives.
Keywords: stochastic equation, invariant measure, ergodic properties of a differentiable measure, logarithmic derivative of a measure, reconstruction of a measure from its logarithmic derivatives. 
@article{TVP_1993_38_3_a11,
     author = {A. I. Kirillov},
     title = {Brownian motion with drift in a {Hilbert} space and its application in integration theory},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {629--634},
     publisher = {mathdoc},
     volume = {38},
     number = {3},
     year = {1993},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1993_38_3_a11/}
}
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A. I. Kirillov. Brownian motion with drift in a Hilbert space and its application in integration theory. Teoriâ veroâtnostej i ee primeneniâ, Tome 38 (1993) no. 3, pp. 629-634. http://geodesic.mathdoc.fr/item/TVP_1993_38_3_a11/