# Questions tagged [stochastic-differential-equations]

Stochastic differential equations (SDE) occur where a system described by differential equations is influenced by random noise. Stochastic differential equations are used in finance (interest rate, stock prices, …), biology (population, epidemics, …), physics (particles in fluids, thermal noise, …), and control and signal processing (controller, filtering, …).

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### differential equations with brownian motion

I have an equation like $dX(t)/dt = f(X(t),t)+\int_{0}^t dW_s$. I was wondering if there is a way to solve it (even in the simple case like $f(X(t),t) = g(X(t))h(t)$). Any hint will be much ...
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### Eigenfrequency of a Duffing oscillator with variable amplitude

I am cross-posting this question here since I didn't get an answer on physics stackexchange. Say I have a duffing oscillator without a driving force or damping: $$\ddot x + \alpha x + \beta x^3 = 0$$...
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### Derivation of unique solution to linear stochastic differential equation

I'm reading up on stochastic differential equations. The form of a linear stochastic differential equation is \begin{equation} dX_t = (AX_t + b)dt + \sigma \ dW_t ; \ X_0 = x_0 \end{equation} We can ...
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### Non-Gaussian Ornstein-Uhlenbeck process and AR(1)

I am looking into generalizing the Ornstein-Uhlenbeck process to non-Gaussian noise sources. In the code, I discretized the OU process (Euler-Maryuama discretization) and converted it into an AR(1) ...
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### Second Moments of linear SDEs

Consider and SDE of the form $$dX = AX\cdot dt + BX\cdot dW_t$$ where $A,B\in\mathbb{R}^2$. How I can calculate the second moments $E[X_1^2]$ and $E[X_2^2]$ of the two variables using Ito's Formula? ...
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### Stationary solution of Fokker-Planck equation for several variables

I am looking for the general stationary solution of the Fokker-Planck equation in two or more dimensions. I know that for the one-dimensional case, given a drift $F(x)$ and position-dependent ...
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### References for an “approximating stochastic optimal control problems deterministically” argument

Assume you have a stochastic control problem : that is, in brief, we have a sample space $(\Omega,F,\mu)$, and a parameter space $U$ (we can take $U = [0,1]$), such that for each $u \in U$ we have a ...
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