On uniqueness and blowup properties for a class of second order SDEs
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Published version
Date
2017-01-01
DOI
Authors
Gomez, Alejandro
Lee, Jong Jun
Mueller, Carl
Neuman, Eyal
Salins, Michael
Version
Accepted manuscript
OA Version
Citation
Alejandro Gomez, Jong Jun Lee, Carl Mueller, Eyal Neuman, Michael Salins. 2017. "On uniqueness and blowup properties for a class of second order SDEs." ELECTRONIC JOURNAL OF PROBABILITY, Volume 22, pp. ? - ? (17). https://doi.org/10.1214/17-EJP95
Abstract
As the first step for approaching the uniqueness and blowup properties of the solutions of the stochastic wave equations with multiplicative noise, we analyze the conditions for the uniqueness and blowup properties of the solution (X๐,Y๐) of the equations dX๐=Y๐dt, dY๐=|X๐|แต
dB๐, (Xโ,Yโ)=(xโ,yโ). In particular, we prove that solutions are nonunique if 0<ฮฑ<1 and (xโ,yโ)=(0,0) and unique if 1/2<ฮฑ and (xโ,yโ)โ (0,0). We also show that blowup in finite time holds if ฮฑ>1 and (xโ,yโ)โ (0,0).
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Attribution 4.0 International