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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.

2 votes
1 answer
178 views

What's the role of commutation relations in stochastic mechanics?

In a stochastic context, we can understand a term like $$ \int_0^T \frac{d q(t)}{dt} dq $$ either as the (Ito) limit $$ \lim_{N\to\infty} \sum_{i}^N dq(t_i) \frac{d q(t_i)}{dt} $$ or the (Anti …
jak's user avatar
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16 votes
2 answers
990 views

Why do stochastic integrals depend on the choice of partitioning points?

When we integrate a function, we must make some choice about how we approximate it before we take the limit. In principle, we can choose $\tau_i$ to be any value between $t_{i-1}$ and $t_i$. But fo …
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