All Questions
Tagged with expected-value stochastic-processes
37
questions
2
votes
0
answers
37
views
Is there a method of analytically solving the expected value of this random variable?
I have the following loss function L where $S_{t}$ represents the price at time t and follows a Geometric Brownian motion. $S_0$ and $r$ are constants.
$$
L = \frac{\sqrt{r}\frac{S_{t}}{S_{o}}-1}{\...
- 141
0
votes
0
answers
23
views
Discrepency between trials and successes for varying probability of success
Suppose there are $N$ balls in an urn, with $X$ white balls and $N-X$ black balls. We perform $k$ iterations of the following process:
Choose a random ball form the urn.
If the ball is white, we put ...
2
votes
1
answer
156
views
What is the expected inverse stopping time for an Brownian Motion?
Let $B_t$ be standard Brownian motion and $\tau_a=\inf\{t\geq 0 : B_t \geq a\}$ be the stopping time where $B_t$ exceeds some value $a$.
Is there an analytic form for $\mathbb{E}\left[\frac{1}{\tau_a}\...
- 780
1
vote
1
answer
61
views
Proving the expectation of a variable in a stochastic process
Problem
Information packets arrive at a server with a poisson process having rate $\lambda = 2$ per hour.
The server processing time for a packet follows the distribution : $f(x) = 1, 0\leq x\leq1$
...
- 53
1
vote
0
answers
115
views
Modeling Urns and Balls System as a Markov Chain
Suppose I have $q$ urns each of which hold up to $n$ distinguishable balls, but only $1$ of each type of ball (there being $n$ types of balls too). I would like to make any particular configuration of ...
- 133
0
votes
0
answers
40
views
What is the expectation of a variable that has two cases (being either 0 or a constant) depending on a normal distributed variable
I need to determine the expectation of a variable: $\mathbb{E}(b(v))$
The value $b$ has two cases: it is either 0 when $v<0$ or a constant c when $v\geq 0$. The value $v$ has a normal distribution.
...
- 29
1
vote
1
answer
184
views
Finding expected value from expectation of squared distance
This problem is actually a part of a much larger biology problem that I am working on. However, I will leave out the unrelated parts.
Consider a sequence of points $\{(x_j, y_j)\}$ where neighboring ...
user319904
2
votes
1
answer
172
views
Expected value of stochastic process given probability of number of sign changes on interval
We have a stochastic process $X_t$, which at a given time $t$ have a value of $-1$ or $1$. Number of sign changes on an interval $(t; t + \Delta)$ have a Poisson distribution $P(N = k) = e^{-\lambda\...
- 167
2
votes
1
answer
658
views
Expected number of running heads in coin toss
How to find the expected number of running heads of a specific length (say 'k' exactly) in 'n' tosses of a coin (fair/biased). For example, consider the output of a coin toss as follows "...
2
votes
1
answer
989
views
Mean and Variance of dot product of 2 random vectors?
x and y are two vectors of dimension k.
Assume that the components of x and y are independent random variables with mean 0 and variance 1. What would be the mean and variance of their dot product, x · ...
- 21
2
votes
1
answer
447
views
Does the unconditional mean of a non stationary ARMA process exist?
Assume that we are dealing with an $\textrm{ARMA}(1,1)$ model:
$$
y_{t} = \theta y_{t-1} + \epsilon_{t} + \alpha \epsilon_{t-1}
$$
where $$ \epsilon_{t} \sim\textrm{ WN}(0, \sigma^{2})
$$
Then, we can ...
user284145
0
votes
1
answer
365
views
Expected value of max of a Stochastic process
Given the Stochastic process
$$X(t) \begin{cases}
A, 0\leq t < \frac{1}{2}\\
B, t \ge \frac{1}{2}
\end{cases}
$$
With $A \sim \mathcal{N}(0, 1)$ and $B \sim \mathcal{N}(1, 1)$.
I'm asked to ...
- 33
1
vote
0
answers
94
views
How to compute the expected number of events in the following conditional renewal process?
I have a stochastic point process with event times $\{x_1, x_2, ...\} $ and I want to compute the expected number of events $n(T)$ over the interval $[0,T]$. The point process is generated as follows:
...
- 286
1
vote
0
answers
111
views
How to show the variance of the inter-arrival time of a Cox process driven by a Poisson process of constant intensity $\lambda$ is $3\lambda$
Ideas on how to show that the variance of a doubly-stochastic Poisson process(aka a Cox process) driven by a homogeneous(stationary) Poisson process of intensity $\lambda$ is $3\lambda$ ?
I've come ...
- 1
3
votes
0
answers
71
views
Multiple interval ratio of E[X / (X + Y)]
I have a sequence of interchanging on- and off-intervals, each pair identified by index $i$. The duration of the on-interval $i$ is represented by random variable $X_i$, and the duration of the off-...
- 31