Problem 2. We consider an N-step random walk with the standard notation seen in class. In partic- ular, we consider the random walk (Sn)A-0 and the standard filtration (Fn)-0. Out of the following processes, determine which ones are (i) adapted; (ii) previsible. • X (1) • • n := max Sj. 0
Problem 2. We consider an N-step random walk with the standard notation seen in class. In partic- ular, we consider the random walk (Sn)A-0 and the standard filtration (Fn)-0. Out of the following processes, determine which ones are (i) adapted; (ii) previsible. • X (1) • • n := max Sj. 0
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![Problem 2.
We consider an N-step random walk with the standard notation seen in class. In partic-
ular, we consider the random walk (Sn)A-0 and the standard filtration (Fn)-0. Out of
the following processes, determine which ones are (i) adapted; (ii) previsible.
• X (1)
•
•
n
:= max Sj.
0<j<n
X(2) = SN - Sn
X(3) = en - n.
X(4)
n
-
1
if Sn-1 Sn-2 = 1,
==
0
N
• X (5)
n
otherwise.
:= E[SN | Fn].
One of them is a martingale, find which.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4a1c925e-790f-448e-9276-e5adcf0e8758%2Fdcc2d351-a7c1-4db4-b433-548b122fdcc8%2Fdwlkdns_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 2.
We consider an N-step random walk with the standard notation seen in class. In partic-
ular, we consider the random walk (Sn)A-0 and the standard filtration (Fn)-0. Out of
the following processes, determine which ones are (i) adapted; (ii) previsible.
• X (1)
•
•
n
:= max Sj.
0<j<n
X(2) = SN - Sn
X(3) = en - n.
X(4)
n
-
1
if Sn-1 Sn-2 = 1,
==
0
N
• X (5)
n
otherwise.
:= E[SN | Fn].
One of them is a martingale, find which.
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