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## 10̃Z~i[

FQOOTNPOPPi΁jPTFOO
ꏊFLwwaaVOP
uҁFgc (dʑ)
ځFHomogenization of diffusions on the lattice ${\mathbf Z}^d$ with periodic drift coefficients, Application of Logarithmic Sobolev inequality vs. weak Poincar{\'e} inequality. (with S. Albeverio, M. Simonetta Bernabei and Michael R{\"o}ckner)
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@A homogenization problem of infinite dimensional diffusion processes indexed by ${\mathbf Z}^d$ having periodic drift coefficients is considered.

By an application of the uniform ergodic theorem for infinite dimensional diffusion processes based on logarithmic Sobolev inequalities, an homogenization property of the processes starting from an almost every arbitrary point in the state space with respect to an invariant measure is proved.

This result is compared with the corresponding weaker homogenization property of the processes proven by applying $L^2$ ergodic theorem based on Poincar{\'e} inequality.

These results are also interpreted as solution to a homogenization problem of infinite dimensional diffusions with random coefficients, which is essentially analogous to the known ones in finite dimensions.

FQOOTNPOQTi΁jPTFOO
ꏊFLwwaaVOP
uҁFc쎁 (L嗝)
ځFL͊wnِ̓ۓƔM͊wF莮Ƃ̉p

## 11̃Z~i[

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uҁFckY (L嗝)
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uҁF{땶 (ޗǈȑ)
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uҁF Y (吔)
ځFA Dynamical Approach to singular Bernoulli Convolutions
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@Bernoulli convolution ͓̏kʑɂ鎩ȑx Ƃēt邪,ł͂̋t̑ʑ(polymorphism) ́uOv̓񕪖؂l@. \beta ݂㐔IiPisot number)̏ꍇ, ̓񕪖؂͉Z̋敪^ꎟ͊wnɂLqł, Bernoulli convolution ̗͂͊wn̕txƂȂ. ̌ʂ

a)Alexander-Zagier formula (\beta ̂Ƃ Bernoulli convolution ̃nEXht̋̓I\j ̗͊wnI߂ƈʉ,y

b)Bernoulli convolution ̃}tN^

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c)Bernoulli convolution ̔^

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## 12̃Z~i[

FQOOTNPQUi΁jPTFOO
ꏊFLwwaaVOP
uҁFckY (L嗝)
ځFPartial observation ɂĐ񊮔s

## 1̃Z~i[

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uҁFc v ()
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