Questions tagged [stochastic-differential-equations]

Stochastic ordinary and partial differential equations generalize the concepts of ordinary and partial differential equations to the setting where the unknown is a stochastic process.

255 questions
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2D Stochastic Navier Stokes equations with Navier boundary condition

For the 2D Stochastic Navier Stokes equations with Navier boundary condition $$du = (\Delta u - u\cdot \nabla u - \nabla p)dt + \Phi dW$$ where we consider additive white noise here. I want to use the ...
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Gradient bound for the Markov semigroup generated by the solution to an Langevin SDE

Let $h\in C^2(\mathbb R)$ with $$h''\ge\rho\tag1$$ for some $\rho>0$ and $$\int\underbrace{e^{-h}}_{=:\:\varrho}\:{\rm d}\lambda=1$$ $\mu$ be the measure with density $\varrho$ with respect to the ...
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Bayesian parameter estimation

I am generally not that knowledgeable for math, so if my question is too broad or inaccurate, please let me know. I am currently reading a paragraph of one paper (https://www.fil.ion.ucl.ac.uk/spm/...
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Application of Gram-Charlier expansion for Swaption pricing with drift extension

I am doing a project for university and I'm stuck at some point. The aim is to implement the Gram-Charlier expansion into the 2-factor Hull-White model with Drift extension. I already found out how ...
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Is an SDE really equal to an integral equation, or is it rather “its integral” that is?

I posted this question on mathstack a couple of weeks ago and even with 100 bounty on it Ive not been able to get any feedback. Hence I tought Id try posting it here. https://math.stackexchange.com/...
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Is there solution to a backward stochastic differential equation with $yz$ in the generator?

Please consider the following backward stochastic differential equation: $$Y(s)=\xi+\int_{s}^{T}a(u)Y(u)+b(u)Y(u)Z(u)du-\int_{s}^{T}Z(u)dW(u)$$ Here $a(s)$, $b(s)$ are square-integrable stochastic ...
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Reference: Stochastic Optimal Control with cost functional

There are a variety of control problems for controlled diffusions $X_t^u$, with the terminal cost given by $$J(u)\triangleq \mathbb{E}\left[g(X_T,u)+\int_0^t h(X_t,u_t)ds\right],$$ function $g$ and ...
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Reference from the article “Random Ordinary Differential Equations”, by J.L. Strand

In the article Random Ordinary Differential Equations, Journal of differential equations 7, 538-553 (1970), by J.L. Strand, reference number 6 refers to his PhD thesis: Stochastic Ordinary ...
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Approximation of deterministic problem with stochastic problem

A lot of problems in PDE theory are solved in the following way: The original problem is quite hard and we can't solve it, so we make the approximation problem that we can solve. Than we go back and ...
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Reference request on connection between PDE problems

I am trying to find references in the literature that connect solutions of any two of the problems given bellow. I study deterministic and stochastic conservation laws. Problems that I am interested ...
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invariant measure theory for spdes with distributional solutions (Hilbert versus Polish)

SPDEs such as the stochastic heat equation for $d\geq 2$ with space-time white noise and the stochastic quantization equation have distributional solutions and we still try to make sense of their ...
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Are Holder Condition and signal to noise ratio (SNR) related?

This question was posted in https://math.stackexchange.com but I got hardly any view. If posting here is an objection please let me know I would delete it immediately. This question has evolved from ...
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Regularity of martingales with respect to spatial parameters

In Stochastic Flows and Stochastic Differential Equations, Kunita is proving in Theorem 3.1.2 that a family $M(t,x)$ of continous local martingales depending on a spatial parameter $x$ takes values in ...
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