# 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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### 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 ...
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-...
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### 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 $1/f$ ...
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?
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### 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 ...
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, ...
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 ...
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-...
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 ...
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 ...
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### 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, ...
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### How to choose a good step size for stochastic gradient descent?

For the purpose of model fitting in a large time series dataset, I am using stochastic gradient descent of the negative log likelihood. The model is nonlinear and non-convex. Is there a thumb rule for ...
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 ...
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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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### 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 ...
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 ...
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 ...
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 ...
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 ...
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### 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 ...