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A lower bound for the transition density function of a stochastic differential equation
Author(s) -
Boyarsky A.
Publication year - 1976
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315270
Subject(s) - stochastic differential equation , bounded function , brownian motion , mathematics , upper and lower bounds , homogeneous , interval (graph theory) , probability density function , differential equation , function (biology) , space (punctuation) , combinatorics , mathematical physics , type (biology) , mathematical analysis , physics , statistics , evolutionary biology , biology , ecology , linguistics , philosophy
Let W t be a one‐dimensional Brownian motion on the probability space (Ω, F,P ), and let dx t = a (x t ) dt + b(x t )dw t , b 2 (x) > 0 , be a one‐dimensional Ito stochastic differential equation. For a(x) = a 0 + a 1 x + … + a n x n on a bounded interval we obtain a lower bound for p(t,x,y) , the transition density function of the homogeneous Markov process x t , depending directly on the coefficients a 0 , a 1 , …, a n , and b(x).