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I would be interested in any book, paper, or other reading material that gives a comprehensive treatment og tilted distributions using the following notion of "tilting" (or equivalent):

Consider the measure space $(\Omega, \mathscr{F}, \mathbb{P}$) and the non-negative measurable function $g$ such that $E(g(X)) < \infty $. Then we can define a new measure $\overline{\mathbb{P}}$ where we define the Radon-Nikodym derivative $\frac{d \overline{\mathbb{P}}}{d \mathbb{P}} = \frac{g(X)}{E(g(X))}$. The distribution of $X$ under this new measure $\overline{\mathbb{P}}$ is biased by the function $g$.

I have been looking for a source that discusses this particular idea, however, in my research most of the material online seems to be focussed on specific distributions. For example, the vast majority of search results are references looking at specific treatments of Exponential Tilting - which is not what I'm after.

I would be grateful for any resources that I could be redirected towards.

I would be interested in any book, paper, or other reading material that gives a comprehensive treatment of tilted distributions using the following notion of "tilting" (or equivalent):

Consider the measure space $(\Omega, \mathscr{F}, \mathbb{P}$) and the non-negative measurable function $g$ such that $E(g(X)) < \infty $. Then we can define a new measure $\overline{\mathbb{P}}$ where we define the Radon-Nikodym derivative $\frac{d \overline{\mathbb{P}}}{d \mathbb{P}} = \frac{g(X)}{E(g(X))}$. The distribution of $X$ under this new measure $\overline{\mathbb{P}}$ is biased by the function $g$.

I have been looking for a source that discusses this particular idea, however, in my research most of the material online seems to be focused on specific distributions. For example, the vast majority of search results are references looking at specific treatments of Exponential Tilting - which is not what I am after.

I would be grateful for any resources that I could be redirected towards.

I would be interested in any book, paper, or other reading material that gives a good introductory treatment to tilted distributions using the following notion of "tilting" (or equivalent):

Consider the measure space $(\Omega, \mathscr{F}, \mathbb{P}$) and the non-negative measurable function $g$ such that $E(g(X)) < \infty $. Then we can define a new measure $\overline{\mathbb{P}}$ where we define the Radon-Nikodym derivative $\frac{d \overline{\mathbb{P}}}{d \mathbb{P}} = \frac{g(X)}{E(g(X))}$. The distribution of $X$ under this new measure $\overline{\mathbb{P}}$ is biased by the function $g$.

I have been looking for a source that discusses this particular idea, however, in my research most of the material online seems to be focussed on specific distributions. For example, the vast majority of search results are references looking at specific treatments of Exponential Tilting - which is not what I'm after.

I would be grateful for any resources that I could be redirected towards.

I would be interested in any book, paper, or other reading material that gives a comprehensive treatment og tilted distributions using the following notion of "tilting" (or equivalent):

Consider the measure space $(\Omega, \mathscr{F}, \mathbb{P}$) and the non-negative measurable function $g$ such that $E(g(X)) < \infty $. Then we can define a new measure $\overline{\mathbb{P}}$ where we define the Radon-Nikodym derivative $\frac{d \overline{\mathbb{P}}}{d \mathbb{P}} = \frac{g(X)}{E(g(X))}$. The distribution of $X$ under this new measure $\overline{\mathbb{P}}$ is biased by the function $g$.

I have been looking for a source that discusses this particular idea, however, in my research most of the material online seems to be focussed on specific distributions. For example, the vast majority of search results are references looking at specific treatments of Exponential Tilting - which is not what I'm after.

I would be grateful for any resources that I could be redirected towards.