LEADER 02945nam 2200481 450 001 9910793620403321 005 20190812131524.0 010 $a1-4704-5255-3 035 $a(CKB)4100000008483129 035 $a(MiAaPQ)EBC5788261 035 $a(PPN)237291118 035 $a(EXLCZ)994100000008483129 100 $a20190628d2019 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aTime changes of the Brownian motion $ePoincare? inequality, heat kernel estimate, and protodistance /$fJun Kigami 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[2019] 210 4$dİ2019 215 $a1 online resource (v, 118 pages) 225 1 $aMemoirs of the American Mathematical Society ;$vVolume 259, Number 1250 311 $a1-4704-3620-5 320 $aIncludes bibliographical references and index. 330 $a"In this memoir, time changes of the Brownian motions on generalized Sierpinski carpets including n-dimensional cube [0, 1]n are studied. Intuitively time change corresponds to alteration to density of the medium where the heat flows. In case of the Brownian motion on [0, 1]n, density of the medium is homogeneous and represented by the Lebesgue measure. Our study includes densities which are singular to the homogeneous one. We establish a rich class of measures called measures having weak exponential decay. This class contains measures which are singular to the homogeneous one such as Liouville measures on [0, 1]2 and self-similar measures. We are going to show the existence of time changed process and associated jointly continuous heat kernel for this class of measures. Furthermore, we obtain diagonal lower and upper estimates of the heat kernel as time tends to 0. In particular, to express the principal part of the lower diagonal heat kernel estimate, we introduce "protodistance"associated with the density as a substitute of ordinary metric. If the density has the volume doubling property with respect to the Euclidean metric, the protodistance is shown to produce metrics under which upper off-diagonal sub- Gaussian heat kernel estimate and lower near diagonal heat kernel estimate will be shown"--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society ;$vVolume 259, Number 1250. 606 $aBrownian motion processes 606 $aMathematical analysis 606 $aHeat$xTransmission 615 0$aBrownian motion processes. 615 0$aMathematical analysis. 615 0$aHeat$xTransmission. 676 $a530.475 686 $a31E05$a60J35$a60J60$a28A80$a30L10$a43A99$a60J65$a80A20$2msc 700 $aKigami$b Jun$065976 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910793620403321 996 $aTime changes of the Brownian motion$93812959 997 $aUNINA