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stochastic process X, is called stationary if {X;} has the sa ibution as {X,+h} for any h > 0. Prove that Brownian mo as stationary increments, i.e. that the process {B+h – B¿} e same distribution for all t.

stochastic process X, is called stationary if {X;} has the sa ibution as {X,+h} for any h > 0. Prove that Brownian mo as stationary increments, i.e. that the process {B+h – B¿} e same distribution for all t.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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2.10. A stochastic process X, is called stationary if {X{} has the same dis- tribution as {X+h} for any h > 0. Prove that Brownian motion B, has stationary increments, i.e. that the process {B,+h – Bt}h20 has the same distribution for all t.
Transcribed Image Text:2.10. A stochastic process X, is called stationary if {X{} has the same dis- tribution as {X+h} for any h > 0. Prove that Brownian motion B, has stationary increments, i.e. that the process {B,+h – Bt}h20 has the same distribution for all t.
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