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Results tagged with stochastic-differential-equations
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user 169474
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
Solution to SDE conditional on high maxima of driving Brownian motion
Partial answer
First, an heuristic argument. When we condition by events with low probability, the main is given by behaviour the less improbable situation. Here we condition by $S_1 := \max_{0 \le s …
- 3,808
0
votes
Accepted
Phase space Brownian bridge
I use capital letters for random variables and small letters for possible values.
Let $W$ be a brownian motion, defined on the canonical space $\mathcal{C}(\mathbb{R}_+)$ endowed with the Wiener measu …
- 3,808
4
votes
Accepted
Integral of $M^\text{*} - M$ with respect to $M^\text{*}$ is zero for $M^\text{*}$ the runni...
The integral with regard do $\mathrm{d}M^*$ is a pathwise Stieltjès integral, so the question is an analysis problem.
Let $f : \mathbb{R}_+ \to \mathbb{R}$ be any continuous function, $F$ its current …
- 3,808