# Questions tagged [stochastic]

For questions regarding the numerical treatment of processes whose behaviors are determined by both deterministic (predictable) and non-deterministic (random) actions.

16 questions with no upvoted or accepted answers
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### 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, ...
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 ...
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, ...
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 ...
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 ...
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 ...
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 ...
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 ...
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}^{-\...
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. ...
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 ...
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 ...