Question: Let .St /t0 be the compound Poisson process with jump distribution Q and intensity > 0. Show that, for fixed t > 0, St

Let .St /t0 be the compound Poisson process with jump distribution Q and intensity

˛ > 0. Show that, for fixed t > 0, St has the distribution

Q = eat M (at)" 2*n n!

Here, Q?0 D ı0 is the Dirac distribution at 0.

Q = eat M (at)" 2*n n!

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Probability Statistics Questions!

Q:

Consider a standard Poisson process \(\left(N_{t} ight)_{t \in[0, T]}\) with intensity \(\lambda>0\) and a standard Brownian motion \(\left(B_{t} ight)_{t \in[0, T]}\) independent of \(\left(N_{t}...

Q:

Let \(\left(N_{t} ight)_{t \in[0, T]}\) be a standard Poisson process started at \(N_{0}=0\), with intensity \(\lambda>0\) under the probability measure \(\mathbb{P}_{\lambda}\), and consider the...

Q:

MUST BE CORRECT ANSWERS A small software company has the following simplified cashflow, funded by shareholders' equity of 20,000 and a bank overdraft of 5000: Invoiced money received 2 months after...

Q:

Microkernel operating systems aim to address perceived modularity and reliability issues in traditional "monolithic" operating systems. (i) Describe the typical architecture of a microkernel...

Q:

QUIZ... Let D be a poset and let f : D D be a monotone function. (i) Give the definition of the least pre-fixed point, fix (f), of f. Show that fix (f) is a fixed point of f. [5 marks] (ii) Show that...

Q:

Positron Emission Tomography Image Reconstruction (Section 1.7.5 of Linear and Nonlinear Programming by Griva-Nash-Sofer, SIAM, 2009) Positron emission tomography (PET) is a medical imaging technique...

Q:

(a) In SystemVerilog, what is the difference between: (i) The ternary operator ? and if...then...else statements? [2 marks] (ii) always_ff and always_comb? [2 marks] (iii) Blocking, non-blocking and...

Q:

Assume that you have an algorithm that can fill 3D triangles with a constant colour. Explain what additional information and additions to the algorithm are required to Gouraud shade the triangles....

Q:

Hello Finstat. I have really appreciated your help so far. Can you help with the attached? From what I can tell and what the instructor has told us is that this is less involved than the previous...

Q:

IOE 419 Mark S. Daskin Service Operations Management IOE Department Winter, 2017 University of Michigan Problem set 4 DUE: MONDAY - February 20, 2017 Points: 100 points total Problem 1: Babette has...

Q:

Suppose that X1, . . . , Xn form a random sample from the exponential distribution with unknown mean . Describe a method for constructing a confidence interval for with a specified confidence...

Q:

An engine with 200 mm cylinder diameter and 300 mm stroke works on theoretical Diesel cycle. The initial pressure and temperature of air used are 1 bar and 27C. The cut-off is 8% of the stroke....

Q:

Required information Problem 7-45 (LO 7-2) (Algo) {The following information applies to the questions displayed below. Matt and Meg Comer are married and file a joint tax return. They do not have any...

Q:

A major strategic alternative for many U.S. firms is to reduce the size of their workforce, i.e., to "downsize." The ethics of downsizing decisions from the employees' perspective was investigated in...