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Chen, Xia

Quenched asymptotics for Brownian motion in generalized Gaussian potential. (English) Zbl 1294.60101

Ann. Probab. 42, No. 2, 576-622 (2014).
The authors summarize the content of this paper in the abstract as follows: We study the long-term asymptotics for the quenched moment consisting of a \(d\)-dimensional Brownian motion and a generalized Gaussian field \(V\). The major progress made in this paper includes: the solution to an open problem posted by R. A. Carmona and S. A. Molchanov [Probab. Theory Relat. Fields 102, No. 4, 433–453 (1995; Zbl 0827.60051)], the quenched laws for Brownian motions in Newtonian-type potentials and in the potentials driven by white noise or by fractional white noise.
Reviewer: Kun Soo Chang (Seoul)

Cited in 14 Documents

MSC:

60J65 Brownian motion
60K37 Processes in random environments
60K40 Other physical applications of random processes
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60F10 Large deviations

Keywords:

generalized Gaussian field; white noise; fractional white noise; Brownian motion; parabolic Anderson model; Feynman-Kac representation

Citations:

Zbl 0827.60051
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\textit{X. Chen}, Ann. Probab. 42, No. 2, 576--622 (2014; Zbl 1294.60101)
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