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Results tagged with stochastic-processes
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user 483817
A stochastic process is a collection of random variables usually indexed by a totally ordered set.
3
votes
1
answer
203
views
Derivation of a series expansion
I am trying to derive the critical coupling strength for synchronisation in a network of phase oscillators with noisy input.
I am following the steps outlined in
Sakaguchi, Hidetsugu. "Cooperative phe …
2
votes
1
answer
418
views
Textbook definition for "path measure" or "probability measure over paths"
I need a formal definition for the path measure for stochastic differential equations.
Which textbook or paper should I consult?
1
vote
1
answer
579
views
Expectation of stochastic integral
Let us consider a diffusion process defined as $dX_t = g(X_t,t) \, dt + \sigma \, dW_t$ which induces a path measure $Q$ in the time interval $[0,T]$.
Is the following expectation
$$ \left\langle \int …
1
vote
1
answer
547
views
Is there an inverse Lamperti transformation for diffusions?
The Lamperti transformation is commonly used to transform SDEs with state dependent coefficients into SDEs with constant diffusion.
For multidimensional processes there are some conditions on the drif …
2
votes
1
answer
200
views
Comparing diffusion processes in different metrics
I would like to know if it is possible to compare two diffusion processes defined on the same manifold $\mathcal{M}$ but with respect to different metrics say $g_1$ and $g_2$.
Is there a way to apply …
5
votes
1
answer
504
views
Riemannian metric induced by a stochastic differential equation
Following this paper, a diffusion process in $\mathcal{R}^d$
$$dX_t = f(X_t) \, dt + \sigma(X_t) \, dW_t ,$$
with $\sigma(x) \in \mathbb{R}^{d \times m}$ and $m$ dimensional Brownian motion can be con …
1
vote
Accepted
Riemannian metric induced by a stochastic differential equation
What is missing above perspective is that by adding drift the most probable path for a diffusion is