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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0answers
27 views

Recommend route for research in numerical backward stochastic differential equation

I am a first year master student. My supervisor assigned numerical backward SDE as my master thesis topic and let me read a thesis from his former PHD student. After finishing reading the thesis, I ...
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1answer
47 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 $1/f$ ...
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0answers
59 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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0answers
41 views

stochastic optimization with unknown distribution

I have a stochastic optimization problem in which I have expectation in constraints. we do not have any any information about distribution function of the random variable a prior. I know in cases you ...
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0answers
32 views

Dynamic programming as final value problem?

I refer to the note "Stochastic systems" by Geering, Dondi, Herzog, Keel (freely available as a pdf ); We consider a stochastic optimal control problem, i.e. given a dynamical system with state ...
3
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1answer
94 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 ...
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0answers
187 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 ...
2
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1answer
79 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 ...
2
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2answers
96 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 ...
2
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2answers
333 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 ...
3
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1answer
232 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{ ...
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0answers
55 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 ...
4
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2answers
334 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 ...
10
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2answers
181 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 ...
4
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2answers
158 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 ...
2
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1answer
158 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 ...
5
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0answers
297 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, ...
4
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2answers
676 views

Differences between “least square”, “mean square” and “least mean square”?

I was wondering what differences are between the terminology: "least square (LS)" "mean square (MS)" and "least mean square (LMS)"? I get confused when reading in Spall's Introduction to Stochastic ...
0
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3answers
179 views

Translating from SBML to Petri Net (matrix representation)

Is there a piece of software that can easily take a representation of a biochemical network from a SBML file and translate it into a Petri Net? Specifically, I'm looking for something that can give ...
3
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1answer
119 views

Introduction for (numerical) linear algebra of random variables

I am in search of an introduction into numerical linear algebra - or, at least, pure linear algebra - that treats the case when the input data are random variables. A typical application would be to ...
2
votes
1answer
61 views

Optimal sample size for Stochastic Steepest Descent

Suppose $g(x_{1:n})$ is the estimate of a gradient, which is calculated at each step of a Stochastic Steepest Descent algorithm. A dataset $x_{1:n}$ is simulated at each step, so if $n$ is small the ...
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4answers
800 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 ...
3
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1answer
272 views

Where can I find coded examples of stochastic collocation applied to an elliptical PDE using smolyak sampling?

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 ...
3
votes
1answer
165 views

Sampling strategies to solve a stochastic partial differential equation

Suppose I had a stochastic partial differential equation of the form: $\nabla^2U=F(x,D)$, where $x\in\Omega\equiv [0,1]$ and $F(x,D)$ is a function which depends on position $x$ and a uniform random ...
4
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3answers
3k views

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 ...
5
votes
2answers
439 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 ...
4
votes
1answer
198 views

Convert ODE into discrete probabilistic model

how can I turn an ODE equation into a discrete probabilistic model? I take for example the Verhulst equation for the growth of a population. $$\frac{dP}{dt} = rP(1-P/K)$$ I was thinking to simulate ...
4
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0answers
138 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?