# 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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### 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 ...
197 views

### 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 ...
I am trying to solve a system of non-linear index-1 DAEs in which the derivatives of the state variables, $x(t)$ are corrupted by additive noise, $w(t)$ (whose co-variance matrix is known). $\dot x(t)... 2answers 316 views ### Runge Kutta and Milstein – system of second-order coupled differential equations with noise I would like to solve a system of second-order differential equations to describe the dynamics of a system of particles. Two Newton-like forces are responsible for the motion of each particle$i$: A ... 0answers 30 views ### Markov chain Monte Carlo with stopping time I asked the same question two days ago on MSE, but received no answer. So I post it here in hope to get any suggestion. As long as I have answer, I will close the other one. Let$(X_t)$be a ... 1answer 46 views ### Adaptive Runge-Kutta for Stochastic (Projected) Gross-Pitaevskii Equation I am using the XMDS library for solving the stochastic (projected) Gross-Pitaevskii equation $$i \hbar \partial \Phi\left(\mathbf{r},t\right)_t=\hat{\mathcal{P}}\left\{(1-i \gamma)\left(\hat{H}_{\... 1answer 117 views ### Numerically solving nonlinear parabolic stochastic PDEs For a project I'm doing, I have to numerically solve a nonlinear parabolic stochastic partial differential equation, of the form$$ u_t = u_{xx} + f(u)(u_x)^2 + a(u) + b(u)W(t, x), $$where primes ... 4answers 5k views ### Algorithm for high quality 1/f noise? How can I generate arbitrarily high quality 1/f noise, for use in a model? My model involves a lot of feedback, over a large number of iterations, with a very high bandwidth, so I'd like the 1/f ... 0answers 20 views ### How to use the solution of a multistage stochastic program? Given a multistage stochastic program, its solution (if it exists) consists of the first decision vector, as well as all the recourse decision vectors for all possible scenarios of an event tree. But ... 0answers 20 views ### Effective fitness formula in the Moran process on a game I was recently reading some literature about evolutionary game theory and I got particularly interested in Moran process linked to prisoner's dilemma as a model of evolution of two sub-populations. ... 0answers 81 views ### Probability approximation: monte carlo VS sde I have a probability measure \mu (say, in \mathbb{R}^{d}, with density) and I want to approximate it numerically. Today I noticed that my measure is ergotic for a certain Stochastic Differential ... 0answers 70 views ### Numerical integration of SDE: choice of dt and algorithm I am working on the following Stochastic Differential Equation (SDE) in the Quantum Mechanics context:$$dX_{t} = a X_{t} dt + b X_{t} dW$$where X_{t} is my stochastic varible, dt is my ... 0answers 65 views ### Solving a nonlinear equation with a Markov process and RVs Assume that we have the following equation and the following assumption. The scope is to solve for some particular variables expressed later. Update$$E_{t}\left[ b(A_{t+1})^{1-\gamma} *R_{t+1}^{-\... 1answer 56 views ### 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: $$\frac{du}{dt} = \nabla(\mathbf{D}_{\gamma} \nabla u) + u(1-... 1answer 204 views ### Solving a nonlinear equation with random variable I would like to solve an equation that looks like this UPDATE E[(R^{1-\gamma})(r_k+\theta-r_z)]=0 , where R=\phi r_z+(1-\phi)(r_k+\theta) and \phi\in[0,1], \theta, is a random variable ... 1answer 401 views ### Simultaneously maximize and minimize I am virtually new to optimization (saw it years ago in a very shallow course) and now I came across a problem that I believe would require from it. The problem is I don't know exactly how to proceed. ... 1answer 71 views ### How to get started with numerically solving a Stochastic Navier Stokes equation I originally posted the question on the math stackexchange, and was told I should try here. I’m researching Stochastic PDE, in particular the Navier Stokes Equation, and would like to estimate the ... 4answers 3k views ### Simulated Annealing proof of convergence I implemented downhill simplex simulated annealing algorithm. Algorithm is very hard to tune, w.r.t. parameters including cooling schedule, starting temperature... My first question is about ... 0answers 40 views ### Is this a form of stochastic gradient descent? I want to minimize the following with respect to parameters B.$$\sum_{k = 1}^{K} f(A_{k}, B)$$where A_k are K different data-sets and B is a matrix of parameters. Can I do this by a ... 0answers 47 views ### How to determine the order of convergence of the Euler-Maruyama method? This question is originally posted in Quant.StackExchange but has been unanswered for some time so I ask in here. To make this simple let us consider the Geometric Brownian Motions (GBM). My ... 0answers 35 views ### Stochastic conjugate directions to improve convergence in narrow valleys My question concerns a specific statement in this paper: N. N. Schraudolph and T. Graepel, "Conjugate Directions for Stochastic Gradient Descent," in Int. Conf. Artificial Neural Networks, Berlin, ... 1answer 120 views ### Jump-Diffusion process: practical solver beyond Euler method? A jump-diffusion process is a stochastic process where both continuous noise (in my case complex Wiener noise dZ,dZ^* such that dZ^2=dZ^{*2}=0,|dZ|^2=dt) and discrete Jumps (in my case Poissonian ... 1answer 98 views ### Computation of the heat kernel from Brownian motion This question is rather simple but I have some difficulties to find code. Let us suppose that I wrote a routine, in a given language, that computes the evolution of a particle doing Brownian motion in ... 1answer 43 views ### Implementation of stochastic cellular automata In my problem, I have a lattice with a stochastic cellular automaton. In order to simplify a bit, let's say it is 1D. In my system, each node can be type A, B or C. A way to represent the system and ... 1answer 127 views ### How is KDE used in stochastic tomography I am currently writing my masters thesis and my topic also touches on Stochastic Tomography for volume reconstruction presented in this paper. Now i understand most of the process described, but i ... 1answer 60 views ### Linear programming with stochasticity? Suppose I have implemented an LP, where some constraint coefficients are implemented as the mean of some probability distribution. Now, I would like to solve the same problem but with stochasticity ... 2answers 198 views ### What’s so great about derivative-free solvers for SDEs? I am trying to familiarise myself with SDEs and have been reading a few review papers on the topic. They leave the impression that a great deal of work has been put into solvers that are derivative-... 0answers 121 views ### Stochastic gradient descent for large deterministic optimization problems The Wikipedia page for SGD describes optimizing a function f = \sum f_i(\theta;x_i) by successively approximating gradients from random subsets of the data, while most literature poses the problem ... 2answers 1k views ### What is the deterministic counterpart of Robbins-Monro algorithm? From Wikipedia, assume that we have a function M(x), and we want to solve the equation M(x) = 0. But we cannot directly observe the function M(x), we can instead obtain measurements of the ... 0answers 66 views ### Global optimization with known distributions of some variables I'm solving simple single-objective multidimensional global optimization problem using various stochastic algorithms like Monte-Carlo, GA and other evolutionary approaches. The task is formulated as ... 1answer 71 views ### From deterministic to stochastic LP formulations I am having a hard time understanding the very first example in "A Tutorial on Stochastic Programming". More specifically the authors show that one can formulate the stochastic variant of (1.2) ... 2answers 140 views ### What kind of optimisation algorithm is suitable for a computationally expensive function? I have a reference value R and a modelled value M. M is generated using a stochastic algorithm with parameters a and b. The objective is to tune a and b so that M is as close as R ... 1answer 158 views ### Problem with Richardson extrapolation method for weak convergence in SDE I have implemented the Richardson extrapolation of the Euler-Maruyama method to 4th order, to estimate the moments of SDE. The Euler-Maruyama works, and I would expect the Richardson extrapolation to ... 1answer 341 views ### Richardson extrapolation for strong rate of convergence of SDE Is it possible to apply Richardson extrapolation with Euler-Maruyama scheme to improve strong rate of convergence of stochastic differential equations? 1answer 1k views ### Solving second order SDE with Gaussian white noise for first time derivative in Matlab I'm having trouble solving a second order differential equation with Gaussian white noise. The equation I'm solving follows the form:$$Ax'' + Bx' + \sin(x) = i + i_{n}$$where i_{n} is the ... 0answers 94 views ### non convex, non linear optimization involving matrix differential equation solution I'm trying to develop an inferential procedure for a multivariate dependent Markov process. Basically, the procedure could be considered as a non linear regression, with a known dependence structure ... 2answers 1k views ### Examples of numerical solution of stochastic differential equation(SDE)? I want to simulate a nonlinear stochastic differential equation$$ {\rm d}X_t = f(X_t) {\rm d}t + g(X_t){\rm d}B_t $$where f,g \in C^{\infty}({\mathbb R}^n ,{\mathbb R}) and B_t is one-... 0answers 638 views ### Stochastic Galerkin projection approach for using generalized polynomial chaos expansion (GPCE) in solving PDE I want to know if there is any way to define the test and trial function in the way that I want instead of using the default functions. So if I want define the polynomial and basis and coefficient, ... 0answers 82 views ### How to fix time intervals to store data in a stochastic simulation (continous time markov chain) I am using FORTRAN to implement Gillespie's stochastic simulation algorithm. I would be running many simulations in parallel (both parallel instances with different seed and parallel functions); if I ... 0answers 2k views ### How to solve an ode with stochastic time-dependent input I am trying to repeat an example I found in a paper. I have to solve this ODE: 25 \ddot{x} + 15 \dot{x} + 330000 x = p(t) where p(t) is a white noise sequence band-limited into the 10-25 Hz ... 1answer 964 views ### How to integrate numerically a function with error bars? Typically, the function that one wants to integrate numerically, f, is given, i.e. its values for various points \{x_i\} are known precisely. The resulting error is due to the fact that we chose a ... 1answer 348 views ### Is Langevin thermostat/equation correct when trying to model time-dependent behaviour of a molecule? I've been taught that when simulating a biomolecule in thermal equilibrium, it's best to use the Langevin thermostat - an algorithm which produces a trajectory, which is a realization of a stochastic ... 2answers 306 views ### Extracting time scales information from empirical cumulative distribution function I have a stochastic process (a Markov chain actually) that has two absorbing states. I am using a difference equation to calculate the first passage time to either of the absorbing states. There are ... 2answers 2k views ### visualization of 3D probability flow I have a master equation for P(N_A^+,N_B^+,N_C^+,t), with N_A^+,N_B^+,N_C^+ all discrete. The numerical integration is done by this Matlab program using Euler's method. Despite the crude Euler's ... 2answers 507 views ### Numerical method for equation solving that works on stochastically computed functions There are many well known numerical methods for solving equations of the type$$ f(x) = 0, \quad x \in \mathbb{R}^n,$$e.g. bisection method, Newton's method, etc. In my application f(x) is ... 1answer 429 views ### Slight mistake in Stochastic Galerkin code I'm following Paul Constantine's Primer on Stochastic Galerkin Method, Section 3.1 (2D Poisson Example). In this matlab code, the example attempts to solve the PDE$$\alpha(w)(u_{xx}+u_{yy})=1 \text{ ... 0answers 81 views ### Stochastic Collocation for time evolving ODE For an Stochastic Differential Equation, e.g., $$\frac{du}{dt} = \alpha*\sin(u*t)$$ where$\alpha$is normally distributed with nonzero mean, I am trying to use a stochastic collocation approach ... 2answers 272 views ### Convergence tests in Markov Chain Monte Carlo For a relatively simple Markov chain Monte Carlo process, such as using Metropolis to find calculate thermal averages for an Ising model, how is it possible to determine whether quantities have ... 1answer 172 views ### How to solve this numerical technique problem? Well, in a numerical technique test we were given the following problem: A physical phenomenon is modeled such that,$F(f,d) = A(f)/d^2 + L$; Where,$F$is a function of frequency$f$and distance$...
I'm having some troubles implementing a collocation method to solve a stochastic partial differential equation of the form: $\nabla (a(x,w)\nabla u(x,w))=f(x,w)$ in $D$, $u=g$ in $\partial D$ where \$...