Probability Density Function of Random Variable
I have the jump Markov process $(N_z)_{zgeq0}$ which behaves like a symmetric random walk on teh set of positive integers. For $z$ large enough, $N_z=0$ where $0$ is an absorbing state. I now define a random variable:
$T_infty = 2int_{0}^{infty}N_z dz$
I want to write the probability density function $P^{infty}_p$ of the random variable $T_infty$, with the initial condition $N_0 = p$. I then want to show it satisfies the differential equation
$frac{dP^{infty}_p}{dtau} = frac{p}{2}(P^{infty}_{p+1}-2P^{infty}_p)+P^{infty}_{p-1}),$ where $pgeq1.$
How do I tackle this?
calculus probability differential-equations random-variables
asked Nov 20 at 11:34
kroneckerdel69
85
add a comment |
I have the jump Markov process $(N_z)_{zgeq0}$ which behaves like a symmetric random walk on teh set of positive integers. For $z$ large enough, $N_z=0$ where $0$ is an absorbing state. I now define a random variable:
$T_infty = 2int_{0}^{infty}N_z dz$
I want to write the probability density function $P^{infty}_p$ of the random variable $T_infty$, with the initial condition $N_0 = p$. I then want to show it satisfies the differential equation
$frac{dP^{infty}_p}{dtau} = frac{p}{2}(P^{infty}_{p+1}-2P^{infty}_p)+P^{infty}_{p-1}),$ where $pgeq1.$
How do I tackle this?
calculus probability differential-equations random-variables
asked Nov 20 at 11:34
kroneckerdel69
85
add a comment |
I have the jump Markov process $(N_z)_{zgeq0}$ which behaves like a symmetric random walk on teh set of positive integers. For $z$ large enough, $N_z=0$ where $0$ is an absorbing state. I now define a random variable:
$T_infty = 2int_{0}^{infty}N_z dz$
I want to write the probability density function $P^{infty}_p$ of the random variable $T_infty$, with the initial condition $N_0 = p$. I then want to show it satisfies the differential equation
$frac{dP^{infty}_p}{dtau} = frac{p}{2}(P^{infty}_{p+1}-2P^{infty}_p)+P^{infty}_{p-1}),$ where $pgeq1.$
How do I tackle this?
calculus probability differential-equations random-variables
asked Nov 20 at 11:34
kroneckerdel69
85
I have the jump Markov process $(N_z)_{zgeq0}$ which behaves like a symmetric random walk on teh set of positive integers. For $z$ large enough, $N_z=0$ where $0$ is an absorbing state. I now define a random variable:
$T_infty = 2int_{0}^{infty}N_z dz$
I want to write the probability density function $P^{infty}_p$ of the random variable $T_infty$, with the initial condition $N_0 = p$. I then want to show it satisfies the differential equation
$frac{dP^{infty}_p}{dtau} = frac{p}{2}(P^{infty}_{p+1}-2P^{infty}_p)+P^{infty}_{p-1}),$ where $pgeq1.$
How do I tackle this?
calculus probability differential-equations random-variables
calculus probability differential-equations random-variables
asked Nov 20 at 11:34
kroneckerdel69
85
asked Nov 20 at 11:34
kroneckerdel69
85
asked Nov 20 at 11:34
kroneckerdel69
85
asked Nov 20 at 11:34
kroneckerdel69
85
asked Nov 20 at 11:34
kroneckerdel69
85
85
add a comment |
add a comment |
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3006212%2fprobability-density-function-of-random-variable%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3006212%2fprobability-density-function-of-random-variable%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
