Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

A random process {X(t),t T} is said to be a Markov process if P {X(t_n+1) x_n+1|X(t_1) = x1, X(t2) = x2, ..., X(t_n) = x_n}

A random process {X(t),t T} is said to be a Markov process if P {X(t_n+1) x_n+1|X(t_1) = x1, X(t2) = x2, ..., X(t_n) = x_n} = P {X(t_n+1) x_n+1|X(t_n) = x_n} whenever t_1 < t_2 <....

a) Show that this definition is actually equivalent to the following. A random process {X(t),t T} is said to be a Markov process if

P {X(t_n+1) x_n+1|X(t1) x1, X(t2) x2, ..., X(t_n) x_n} = P {X(t_n+1) x_n+1|X(t_n) x_n} whenever t_1 < t_2 <....< t_n < t_n+1

b) Use this fact to show that for a Markov process {X(t),t T}, the second-order distribution is sufficient to completely characterize the random process X(t). c) Show that any process with independent increments must be a Markov process.

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

Corporate Finance Theory And Practice

Authors: Aswath Damodaran

2nd Edition

0471283320, 9780471283324

More Books

Students also viewed these Finance questions

Question

Analyze the role of language processing in cognitive psychology.

Answered: 1 week ago

Question

=+3. How will you measure action objective?

Answered: 1 week ago

Question

=+2. What research methodologies would be most effective?

Answered: 1 week ago

Question

=+ Focus groups with representative publics. Which publics?

Answered: 1 week ago