# Upper and Lower Bounds in Exponential Tauberian Theorems

@article{Voss2009UpperAL, title={Upper and Lower Bounds in Exponential Tauberian Theorems}, author={Jochen Voss}, journal={arXiv: Probability}, year={2009}, pages={41-50} }

In this text we study, for positive random variables, the relation between the behaviour of the Laplace transform near infinity and the distribution near zero. A result of De Bruijn shows that $E(e^{-\lambda X}) \sim \exp(r\lambda^\alpha)$ for $\lambda\to\infty$ and $P(X\leq\epsilon) \sim \exp(s/\epsilon^\beta)$ for $\epsilon\downarrow0$ are in some sense equivalent (for $1/\alpha = 1/\beta + 1$) and gives a relation between the constants $r$ and $s$. We illustrate how this result can be used… CONTINUE READING

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#### References

##### Publications referenced by this paper.

SHOWING 1-9 OF 9 REFERENCES

## Regular variation in

VIEW 2 EXCERPTS

HIGHLY INFLUENTIAL

## Tauberian Theory: A Century of Developments

VIEW 2 EXCERPTS

## Some Large Deviation Results for Diffusion Processes

VIEW 2 EXCERPTS

## Handbook of Brownian Motion: Facts and Formulae

VIEW 1 EXCERPT

HIGHLY INFLUENTIAL

## Large Deviations Techniques and Applications, volume 38 of Applications of Mathematics

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## Tauberian theorems and large

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL