Tutorial on Additive Levy´ ProcessesLecture #1Davar KhoshnevisanDepartment of MathematicsUniversity of Utahhttp://www.math.utah.edu/˜davarInternational Conference on Stochastic Analysisand Its ApplicationsAugust 7–11, 2006D. Khoshnevisan (Salt Lake City, Utah) ICSAA, Seattle ’06 1 / 20N NCould have R in place of R , etc.+dX ,..., X independent Brownian motions in R .1 N“Additive Brownian motion”:NX(t) := X (t )+···+ X (t ) for all t = (t ,..., t )∈ R .1 1 N N 1 N +Likewise, can have “additive stable,” “additive Levy´ ,” etc.IntroductionSome TerminologyAn “(N, d) random field” X has N parameters and takes values indR (Adler, 1981);d Ni.e., X(t)∈ R for all t := (t ,..., t )∈ R .1 ND. Khoshnevisan (Salt Lake City, Utah) ICSAA, Seattle ’06 2 / 20dX ,..., X independent Brownian motions in R .1 N“Additive Brownian motion”:NX(t) := X (t )+···+ X (t ) for all t = (t ,..., t )∈ R .1 1 N N 1 N +Likewise, can have “additive stable,” “additive Levy´ ,” etc.IntroductionSome TerminologyAn “(N, d) random field” X has N parameters and takes values indR (Adler, 1981);d Ni.e., X(t)∈ R for all t := (t ,..., t )∈ R .1 NN NCould have R in place of R , etc.+D. Khoshnevisan (Salt Lake City, Utah) ICSAA, Seattle ’06 2 / 20Likewise, can have “additive stable,” “additive Levy´ ,” etc.IntroductionSome TerminologyAn “(N, d) random field” X has N parameters and takes values indR (Adler, 1981);d Ni.e., X(t)∈ R for all t := (t ,..., t )∈ R .1 NN NCould have R in ...