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I need a formal definition for the path measure for stochastic differential equations. Which textbook or paper should I consult?

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 …

What is missing above perspective is that by adding drift the most probable path for a diffusion is

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 …

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 …

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 …

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 …