02945nam 2200481 450 991081140310332120190812131524.01-4704-5255-3(CKB)4100000008483129(MiAaPQ)EBC5788261(PPN)237291118(EXLCZ)99410000000848312920190628d2019 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierTime changes of the Brownian motion Poincaré inequality, heat kernel estimate, and protodistance /Jun KigamiProvidence, Rhode Island :American Mathematical Society,[2019]©20191 online resource (v, 118 pages)Memoirs of the American Mathematical Society ;Volume 259, Number 12501-4704-3620-5 Includes bibliographical references and index."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"--Provided by publisher.Memoirs of the American Mathematical Society ;Volume 259, Number 1250.Brownian motion processesMathematical analysisHeatTransmissionBrownian motion processes.Mathematical analysis.HeatTransmission.530.47531E0560J3560J6028A8030L1043A9960J6580A20mscKigami Jun65976MiAaPQMiAaPQMiAaPQBOOK9910811403103321Time changes of the Brownian motion3955603UNINA