TY - JOUR
T1 - Stochastic Newton equation in strong potential limit
AU - Liang, Song
N1 - Funding Information:
The author would like to thank Professor Sergio Albeverio for reading and making comments on the manuscript. Also, the author wish to acknowledge the anonymous referees for their detailed and helpful comments to the manuscript, which substantially improved the quality of this paper. This research is financially supported by Grant-in-Aid for the Encouragement of Young Scientists (No. 25800056 ), Japan Society for the Promotion of Science .
Publisher Copyright:
© 2016 Elsevier B.V.
PY - 2016/10/1
Y1 - 2016/10/1
N2 - We consider a type of stochastic Newton equations, with single-well potential functions, and study the limiting behaviors of their solution processes when the coefficients of the potentials diverge to infinity. We prove that for dimension 1, the stochastic solution processes converge. The explicit descriptions of the limiting processes are also given. Especially, the limiting processes are deterministic for special initial conditions.
AB - We consider a type of stochastic Newton equations, with single-well potential functions, and study the limiting behaviors of their solution processes when the coefficients of the potentials diverge to infinity. We prove that for dimension 1, the stochastic solution processes converge. The explicit descriptions of the limiting processes are also given. Especially, the limiting processes are deterministic for special initial conditions.
KW - Convergence
KW - Diffusion
KW - Potential
KW - Stochastic Newton equation
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U2 - 10.1016/j.spa.2016.03.007
DO - 10.1016/j.spa.2016.03.007
M3 - Article
AN - SCOPUS:84962013798
SN - 0304-4149
VL - 126
SP - 2913
EP - 2955
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
IS - 10
ER -