On uniqueness and blowup properties for a class of second order SDEs
Lee, Jong Jun
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Citation (published version)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
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 (X𝗍,Y𝗍) of the equations dX𝗍=Y𝗍dt, dY𝗍=|X𝗍|ᵅdB𝗍, (X₀,Y₀)=(x₀,y₀). In particular, we prove that solutions are nonunique if 0<α<1 and (x₀,y₀)=(0,0) and unique if 1/2<α and (x₀,y₀)≠(0,0). We also show that blowup in finite time holds if α>1 and (x₀,y₀)≠(0,0).
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