Show that N+ is continuous in probability, i.e. for any arbitrarily small € > 0, P{|N₁ − Ns| > ε } → 0, as s→ t. Hint. Use the stationary increments property (N₂ - N₁ ~ Nts if s≤t) and notice that Nu > ε is the same as Nu > 0 for small ε. (Why?)
Show that N+ is continuous in probability, i.e. for any arbitrarily small € > 0, P{|N₁ − Ns| > ε } → 0, as s→ t. Hint. Use the stationary increments property (N₂ - N₁ ~ Nts if s≤t) and notice that Nu > ε is the same as Nu > 0 for small ε. (Why?)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 23E
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Please help solve this question. A hint to use within the work is provided. This is an ungraded lecture question that I would love to know how to do!
Transcribed Image Text:Show that N is continuous in probability, i.e. for any arbitrarily small € > 0,
P{|Nt — Ns| > ɛ} → 0, as s → t.
Hint. Use the stationary increments property (№ — N3 ~ №−s if s≤ t) and notice that N > ε is the
same as Nu > 0 for small ε. (Why?)
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