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Results tagged with stochastic-differential-equations
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user 163454
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.
1
vote
0
answers
172
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Adiabatic elimination of "fast"/"velocity" variable
My question comes from section IV, part A of the paper titled Stochastic resonance. Specifically, their equation (4.1) states that, if we start with a Langevin equation of the form $$m\ddot{x} = -m\ga …
- 730
4
votes
1
answer
335
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Reference request: showing that solution of an Ito SDE stays bounded with positive probability
Assume that we have a (well-posed) Ito SDE of the form $$\mathrm{d} X_t = b(X_t)\,\mathrm{d} t + \sigma(X_t)\,\mathrm{d}W_t \label{1}\tag{1},$$ where $b \colon \mathbb{R}^d \to \mathbb{R}^d$, $\sigma …
- 730
5
votes
1
answer
640
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Random time change from Oksendal's SDE textbook
I have two questions related to the random time change introduced in Oksendal's textbook on SDEs (page 155-156). Specifically, for Lemma 8.5.6., I have no clue as to why we should define $t_j$ in te …
- 730
1
vote
1
answer
263
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consequence of "the best coupling" of two SDEs with different diffusion matrices
My question comes form a potion of the long review paper, which is attached below
In the set-up, $\sigma_1$ and $\sigma_2$ are possibly different, constant diffusion matrices. To my knowledge, if we …
- 730
2
votes
0
answers
101
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Relations between different "propagation of chaos" type results?
My questions come from the paper Logarithmic Sobolev inequalities for some
nonlinear PDE’s written by F. Malrieu (May 2001). The basic set-up is that we have a $N$-particle system $(X^{i,N}_t)_{1\leq …
- 730