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Results tagged with stochastic-calculus
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user 483817
Stochastic calculus provides a consistent theory of integration for stochastic processes and is used to model random systems. Its applications range from statistical physics to quantitative finance.
1
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1
answer
579
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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
$$ \left\langle \int …
1
vote
1
answer
547
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Is there an inverse Lamperti transformation for diffusions?
The Lamperti transformation is commonly used to transform SDEs with state dependent coefficients into SDEs with constant diffusion.
For multidimensional processes there are some conditions on the drif …
2
votes
1
answer
200
views
Comparing diffusion processes in different metrics
I would like to know if it is possible to compare two diffusion processes defined on the same manifold $\mathcal{M}$ but with respect to different metrics say $g_1$ and $g_2$.
Is there a way to apply …
5
votes
1
answer
504
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Riemannian metric induced by a stochastic differential equation
Following this paper, a diffusion process in $\mathcal{R}^d$
$$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