Tagged Questions

17 views

Simulation Lévy process

I need to simulate a Lévy process from its characteristic triple $(\gamma,\Sigma,\nu)$ where $\nu$ is the Lévy measure. I know that I can simulate it by summing a brownian motion and a compound ...
19 views

Stability of simulation of brownian noise

As I understand, Brownian noise can be simulated by the process $$x_{n+1}=x_n+R_n$$ where $R\sim U[-a,a]$. The expected value for $x_n$ is then $x_0$. But $\text{Var} x_n\to\infty$ as $n\to\infty$ ...
28 views

Calculate expectation under risk neutral measure: $\mathbb{E_Q}(\max(S-1,0))$

I am busy with a numerical simulation and I want the calculate the following expectation under the risk neutral measure: $\mathbb{E_Q}(\max(S-1,0))$. $S$ is some variable that I calculated using ...
66 views

Distribution of time spent above $0$ by a Brownian Bridge.

Let's say I have a Brownian motion, such that I know its value at time 0 (0) and time T (also 0). I am trying to evaluate the time spent above 0 between time 0 and T. Obviously I know that the ...
30 views

simulate hitting time of Brownian motion

let's say I have a brownian motion $W_t$, and I know the value of $W_1$. Is there a way to simulate the hitting time of $W_t$ and a given function $f(t)$ ? For instance I know that if $f(t)$ is a ...
15 views

interpolation linear for a sample path

I am looking for a couple of references: interpolation linear for a sample path of Brownian Motion
17 views

Monte Carlo by point or by interval

Say I compute monte carlo output from input scenarios. Input are discrete time series. I choose time series as an example to make the problem more obvious - this could be also any curve. Computation ...
50 views

Samples from the Dirichlet measure

In Ferguson, 1973, Definition 2, he defines a sample of size $n$ from a random probability measure $G$ on $(\mathcal{X}, \mathcal{B})$ as:  P(X_1 \in C_1, \cdots, X_n \in C_n | G(A_1), \cdots, ...
372 views

Poisson Process, Exponential inter-arrival times simulation conundrum

I am trying to simulate a poisson process by using the fact that the inter-arrival times are distributed as an exponential distribution. I want to generate patient arrival times in (say) 1 hour. So, ...
98 views

Approximation of SDE

I have been struggling with the following problem: If you want to find a numerical result by simulating the paths of a stochastic differential equation, in particular a geometric brownian motion I ...
256 views

Simulation of a Gaussian process on $R^2$ with a stationary kernel using the Karhunen-Loève expansion

Assume $X(\omega, t) \sim \mathcal{N}(0, K(\cdot, \cdot))$ is a real-valued, centered Gaussian process on $R^2$, i.e., $X: \Omega \times R^2 \to R$. Let the covariance function of the process be ...
52 views

How to resolve this?

I've the following problem to model and program it: suppose that we have a central server that provides 3 different services($S_1,S_2,S_3$), there are $N$ machines connected to this server: each ...
54 views

Comparing speed in stochastic processes generated from simulation?

I have an agent-based simulation that generates a time series in its output for my different treatments. I am measuring performance through time, and at each time tick the performance is the mean of ...
119 views

Simulating first passage times

I have a Brownian motion $X_t = \mu t+\sigma W_t$, where $W_t$ standard Brownian motion. I know that the first passage time $\tau = \min\{t|X_t\leq\alpha\}$, is Inverse Gaussian distributed i.e., ...
159 views

Simulation of diffusion processes on the canonical space $C([0,t],\mathbb{R})$

I'm currently reading the article "Exact and computationally efficient likelihood-based estimation for discretely observed diffusion processes" by Beskos, Papaspiliopoulos, Roberts and Fearnhead. I'm ...
162 views

Markov Chains - Using Gibbs & Metropolis algorithm.

Suppose $f_x,_y$ is bivariate normal distribution. I was given the parameters $(μ_1, μ_2, σ_1^2, σ_2^2)$ and $ρ=0.95$ the correlation coefficient. I want to generate \$(x_1,y_1), ...