# Questions tagged [large-deviation-theory]

Use this tag for question on large deviations theory

108 questions
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### Using Girsanov Theorem Backwards?/ Obtaining Radon-Nikodym Derivative

On page 112/133 of Den Hollanders book on Large Deviations he wants to calculate the R.N derivative between two path measures : one is the path measure of the solution to an SDE $dX_t=H(X_t)dt+dW_t$ ...
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### The rate function in large deviations

Why do we use rate functions in the definition of Large Deviations. That is why do we require the function to be lower-semicontinuous?
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### Sum of variables of a martingale

I have the sequence $X_1, X_2,...X_n$ as a martingale, each of which is bounded. Now I want to explore some upper bound for the sum $S_n=X_1+X_2+...+X_n$, e.g., the format like Hoeffding inequality or ...
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### What does it mean that “the central limit theorem does not hold far away from the peak”?

So I know nothing about large deviations theory, and I'm reading some notes. They claim that: The CLT does not hold far away from the peak I am not sure how to parse this statement. There are many ...
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### Good book on large deviations theory

I am interested in reading about large deviations theory. Can anybody please suggest me any good book regarding this. Thanks in advance.
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### Polynomial term for random walk large deviations

Let $S_n = \sum_1^n X_i$ with $P(X_i =1) = p>1/2$ and $P(X_i = -1) = 1-p$ be a biased random walk. Large deviations tell us that $p_0=P(S_n \leq 0) \leq n^a(2 \sqrt{p(1-p)})^n$. We are curious what ...
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### Reference request: Large deviations for a conditional probability

Suppose a sequence of probability measures $(\mathbb P_n)_{n\in\mathbb N}$ on a Polish space $X$ satisfies the large deviations principle with a good rate function $I$ and rate $n$. Informally ...