Geodesic
Deviation Estimates for Random Walks and Stochastic Methods for Solving the Schr\"odinger Equation
Matematičeskie zametki, Tome 76 (2004) no. 4, pp. 610-624

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The stochastic representation of solutions of the Cauchy problem for the Schrödinger equation is used in order to construct unitary matrix approximations of the resolving operator. We show that the probability distribution of deviations of random walks allows one to estimate the increase rate of derivatives and the support of solutions. 
@article{MZM_2004_76_4_a12,
     author = {A. M. Chebotarev and A. V. Polyakov},
     title = {Deviation {Estimates} for {Random} {Walks} and {Stochastic} {Methods} for {Solving} the {Schr\"odinger} {Equation}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {610--624},
     publisher = {mathdoc},
     volume = {76},
     number = {4},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_76_4_a12/}
}
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A. M. Chebotarev; A. V. Polyakov. Deviation Estimates for Random Walks and Stochastic Methods for Solving the Schr\"odinger Equation. Matematičeskie zametki, Tome 76 (2004) no. 4, pp. 610-624. http://geodesic.mathdoc.fr/item/MZM_2004_76_4_a12/