MATH2750: Exercises 2
Examples 2.1 (Gambling Model). In the gambling model of Example 1.4, what is the probability that the game will go on indenitely, i.e. neither of the gamblers will ever be ruined
8
MATH2750: Continuous time MPs
8.1
8.1.1
General processes with discrete states
Denition; Chapman Kolmogorov equations; intensities
Denition. Let state space of the process be S = cfw_1, 2, . . . or
3
MATH2750
3.1
Stochastic process: r.vs which depend on TIME
Any stochastic process is, by denition, a collection of random variables depending on
time, i.e.
Xn , n = 0, 1, . . . , or Xt , t 0.
In mos
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MATH2750: Continuous time MPs
7.1.1. Definition This is a continuous time analogue of the "discrete time jump process" from Handout 2.2, with S = 0, 1, 2, . . . By definition, X0 = 0. Then, the cons
4
4.1
MATH2750
Roulette (gambling): equation on a nite interval
As we already know from the solution of the Exercise 1.4, the gambling process Xn of
the fortune of the rst (say) player is a MP, with t
5
5.1
MATH2750
Stationary (equilibrium) distributions
The notion of stationary distributions relates to a Markov chain understood as a family of processes with the same generator, rather than one proc
MATH2750: Introduction to Markov Processes
Exercises 5
E5.1. Consider a Markov chain on the state space S = cfw_1, 2, 3 with
transition matrix
1
1
1
3
3
3
0
0
P = 0
1
1
0
(a) Draw the transition gra
MATH2750
MATH275001
This question paper consists of 4
printed pages, each of which is
identied by the reference MATH2750.
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UNIVERSITY OF LEEDS
Mock
MATH2750
MATH275001
This question paper consists of 3
printed pages, each of which is
identied by the reference MATH2750.
Only approved basic scientic
calculators may be used.
UNIVERSITY OF LEEDS
Mock