# 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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### Discretization formula for system of differential equations. "Solution to one of these is the initial condition of the other". In which sense?

Consider the following stochastic differential equation $$dy=\left(A-\left(A+B\right)y\right)dt+C\sqrt{y\left(1-y\right)}dW\tag{1}$$ where $A$, $B$ and $C$ are parameters ...
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### Why the renormalization constant of the regularized $2D$ noise diverges as a logarithm

Motivation and overview I'm trying to understand the theory of regularity structures and in particular, following this paper I'm looking to the $\Phi^4_d$ model on the $d$-dimensional torus $T^d$ i....
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### How are Markov Kernels Related to SDEs

(Disclaimer: I've been working with SDEs for some years now but have not worked with general Markov processes before... so I'm trying to reconcile some ideas with this post.) I recently read the ...
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### proving equalities in stochastic calculus

I am struggling with this question: FIRST PART (almost done, but stuck somewhere): Let $Z$~$N(0,1)$ be a standard normal random variable, and define a function $F$ by the formula ...
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Inspired by the result for ODE here, which shows that solutions to the same ODE with different initializations do not intersect, I am wondering if similar results also hold for SDE? Consider the SDE $$... • 361 6 votes 1 answer 58 views ### deriving covariance of SDE from fokker-planck In the book 1 the covariance of an SDE is derived. I am not sure about a particular step. Let me describe it in a TLDR version, then in a longer version. We have an SDE$$dx = f(x,t) dt + L(x,t) d\...
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From this paper, if the deterministic dynamics of $x_t$ is $dx_t=v_tdt$ where $v_t=\nabla\log\pi-\nabla\log\mu_t$ with $\mu_t$ denotes the law of $x_t$ and $\pi$ is a distribution depending on $x_t$, ...