A law of the iterated logarithm for stochastic processes defined by differential equations with a small parameter
| dc.contributor.author | Heunis, A.J. | |
| dc.contributor.author | Kouritzin, Michael | |
| dc.date.accessioned | 2025-05-01T20:56:23Z | |
| dc.date.available | 2025-05-01T20:56:23Z | |
| dc.date.issued | 1994 | |
| dc.description | Consider the following random ordinary differential equation: X˙ϵ(τ)=F(Xϵ(τ),τ/ϵ,ω)subject toXϵ(0)=x0, where {F(x,t,ω),t≥0} are stochastic processes indexed by x in Rd, and the dependence on x is sufficiently regular to ensure that the equation has a unique solution Xϵ(τ,ω) over the interval 0≤τ≤1 for each ϵ>0. Under rather general conditions one can associate with the preceding equation a nonrandom averaged equation: x˙0(τ)=F¯¯¯(x0(τ))subject tox0(0)=x0, such that limϵ→0sup0≤τ≤1E|Xϵ(τ)−x0(τ)|=0. In this article we show that as ϵ→0 the random function (Xϵ(⋅)−x0(⋅))/2ϵloglogϵ−1−−−−−−−−−−√ almost surely converges to and clusters throughout a compact set K of C[0,1]. | |
| dc.identifier.doi | https://doi.org/10.7939/R3KK4H | |
| dc.language.iso | en | |
| dc.relation.isversionof | M.A. Kouritzin and A.J. Heunis, "A law of the iterated logarithm for stochastic processes defined by differential equations with a small parameter'', Annals of Probability, 22(2) (1994) pp. 659-679. | |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/ | |
| dc.subject | Ordinary differential equations | |
| dc.subject | Mixing processes | |
| dc.subject | Law of the iterated logarithm | |
| dc.subject | Central limit theorem | |
| dc.title | A law of the iterated logarithm for stochastic processes defined by differential equations with a small parameter | |
| dc.type | http://purl.org/coar/resource_type/c_6501 http://purl.org/coar/version/c_970fb48d4fbd8a85 | |
| ual.jupiterAccess | http://terms.library.ualberta.ca/public |
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