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Continuous Time Markov Chains Suppose that one particle (created by a chain reaction) enters a space and randomly produces with rate a (a new particle has the same reproduction rate). Let K> 0 be the number (integer) of particles created at time t starting from Ko = 1. Write down the master equation for P₁(t) = P(K₁ = k) and find the so- lution of the master equation starting from P(0) = 8,1. In other words, solve the equation for k = 1 and then for k = 2.

Continuous Time Markov Chains Suppose that one particle (created by a chain reaction) enters a space and randomly produces with rate a (a new particle has the same reproduction rate). Let K> 0 be the number (integer) of particles created at time t starting from Ko = 1. Write down the master equation for P₁(t) = P(K₁ = k) and find the so- lution of the master equation starting from P(0) = 8,1. In other words, solve the equation for k = 1 and then for k = 2.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Extra Question – Class Exercise 6.3 Continuous Time Markov Chains Suppose that one particle (created by a chain reaction) enters a space and randomly produces with rate a (a new particle has the same reproduction rate). Let K, > 0 be the number (integer) of particles created at time t starting from Ko = 1. Write down the master equation for P<(t) = P(K = k) and find the so- lution of the master equation starting from P(0) = dk.1. In other words, solve the equation for k = 1 and then for k = 2. Keep particle creation and annihilation in mind.
Transcribed Image Text:Extra Question – Class Exercise 6.3 Continuous Time Markov Chains Suppose that one particle (created by a chain reaction) enters a space and randomly produces with rate a (a new particle has the same reproduction rate). Let K, > 0 be the number (integer) of particles created at time t starting from Ko = 1. Write down the master equation for P<(t) = P(K = k) and find the so- lution of the master equation starting from P(0) = dk.1. In other words, solve the equation for k = 1 and then for k = 2. Keep particle creation and annihilation in mind.
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