Questions tagged [stochastic]
For questions regarding the numerical treatment of processes whose behaviors are determined by both deterministic (predictable) and non-deterministic (random) actions.
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Why is Magnetic Susceptibility not showing the expected transition in 2D&3D Ising Model?
I'm trying to code the Ising Model with the metropolis algorithm to study the ferromagnetic-paramagnetic transitions. The code seems to work ; the equilibration happens. While equilibrating, the ...
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Simulate Jump-Diffusion $dX_t = \mu(X_t)dt + \sigma(X_t)dW(t) + \int_{\{|c| <1 \}}g(X_t,c)\tilde{N}(dt,dc) + \int_{\{|c| \ge 1 \}}h(X_t,c)N(dt,dc)$
I would like to be able to model an SDE having the form
$$dX_t = \mu(X_t)dt + \sigma(X_t)dW(t) + \int_{\{|c| <1 \}}g(X_t,c)\tilde{N}(dt,dc) + \int_{\{|c| \ge 1 \}}h(X_t,c)N(dt,dc).$$
where $W$ is a ...
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Stochastic cellular automata - algorithm limited by 1 cell per timestep
Context
Let's say I am trying to model the spread of mold in a petri dish, using a stochastic cellular automata approach. The petri dish can be thought of as a grid of 1mm x 1mm squares, each called ...
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Stochastic differential equation system (SDE) : overflow encountered in double-scalars
I'm trying to integrate the following SDE system from Dekker et al. [1]
$$\begin{cases}
\frac{dx}{dt}=a_1x^3+a_2x+\phi+\zeta_x\\
\frac{dy}{dt}=b_1z+b_2(\kappa(x)-(y^2+z^2))y+\zeta_y\\
\frac{dz}{dt}=...
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Rate of convergence - Stochastic Euler Method
The absolute error criterion of the pathwise approximation of an Ito process $X$ by an Euler approximation $Y$ is:
$$
\epsilon=E\left(\left|X_{T}-Y(T)\right|\right)
$$
We shall say that a time-...
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Numerical stability of taking the `mean` of outputs from the simulation of a discrete stochastic dynamical system
I am writing a simulation for a discrete stochastic dynamical system. Since the simulation is stochastic, I need to run the simulation multiple times and then average the values of each timestep. I ...
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Guidelines for publishing data from a stochastic simulation
So, my question is if one should ideally keep a record of all seeds that are used when publishing numerical work that involves one or more random number generators (e.g. a stochastic simulation), and ...
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Adaptive Runge-Kutta for Stochastic (Projected) Gross-Pitaevskii Equation
I am using the XMDS library for solving the stochastic (projected) Gross-Pitaevskii equation
$$i \hbar \partial \Phi\left(\mathbf{r},t\right)_t=\hat{\mathcal{P}}\left\{(1-i \gamma)\left(\hat{H}_{\...
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Numerically solving nonlinear parabolic stochastic PDEs
For a project I'm doing, I have to numerically solve a nonlinear parabolic stochastic partial differential equation, of the form
$$
u_t = u_{xx} + f(u)(u_x)^2 + a(u) + b(u)W(t, x),
$$
where primes ...
user34137
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Effective fitness formula in the Moran process on a game
I was recently reading some literature about evolutionary game theory and I got particularly interested in Moran process linked to prisoner's dilemma as a model of evolution of two sub-populations.
...
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Probability approximation: monte carlo VS sde
I have a probability measure $\mu$ (say, in $\mathbb{R}^{d}$, with density) and I want to approximate it numerically. Today I noticed that my measure is ergotic for a certain Stochastic Differential ...
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Numerical integration of SDE: choice of $dt$ and algorithm
I am working on the following Stochastic Differential Equation (SDE) in the Quantum Mechanics context:
$$dX_{t} = a X_{t} dt + b X_{t} dW$$
where $X_{t}$ is my stochastic varible, $dt$ is my ...
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What is the right way to set up two random tensor fields which have an identical average diffusivity
I want to compare some properties of traveling waves through two randomly diffusive media. The traveling waves follow the fisher equation:
$$\frac{du}{dt} = \nabla(\mathbf{D}_{\gamma} \nabla u) + u(1-...
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How to optimize sampling for parameter estimation
I have a computer model with a number of parameters that need to be calibrated based on experimental results. It's also important to understand the sensitivity of the results to each parameter ...
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How to get started with numerically solving a Stochastic Navier Stokes equation
I originally posted the question on the math stackexchange, and was told I should try here.
I’m researching Stochastic PDE, in particular the Navier Stokes Equation, and would like to estimate the ...
