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Reverse Hoeffding Inequalities

Is there a discrete-time analogue of Doléans-Dade exponential?Generalization of Hoeffding InequalityOptimal Stopping TheoremAzuma inequality with probabilistic bound for the incrementsDoob's inequalities for not necessarily right-continuous martingalesHoeffding Inequality.Generalizing Doob's super-martingale inequalityApplication of Hoeffding inequalityHow to get the following upper and lower bounds of $E[sup_{ngeq 0} M_n]$?A 'reverse' Hoeffding Inequality

0

$begingroup$

Suppose that $X_t$ is a super-martingale, the Hoeffding inquality gives an exponential upper bound on the quatity
$$
mathbb{P}left(
sup_{0 leq tleq T}X_t
geq x
right).
$$

When can a lower-bound be obtained; that is a function of $x$ and $t$ such that
$$
f(t,x)leq mathbb{P}left(
sup_{0 leq tleq T} X_t
geq x
right)?
$$

probability probability-theory large-deviation-theory extreme-value-theorem

share|cite|improve this question

asked Mar 18 at 20:43

AIM_BLBAIM_BLB

2,5392820

$endgroup$

add a comment | 

0

$begingroup$

Suppose that $X_t$ is a super-martingale, the Hoeffding inquality gives an exponential upper bound on the quatity
$$
mathbb{P}left(
sup_{0 leq tleq T}X_t
geq x
right).
$$

When can a lower-bound be obtained; that is a function of $x$ and $t$ such that
$$
f(t,x)leq mathbb{P}left(
sup_{0 leq tleq T} X_t
geq x
right)?
$$

probability probability-theory large-deviation-theory extreme-value-theorem

share|cite|improve this question

asked Mar 18 at 20:43

AIM_BLBAIM_BLB

2,5392820

$endgroup$

add a comment | 

$begingroup$

Suppose that $X_t$ is a super-martingale, the Hoeffding inquality gives an exponential upper bound on the quatity
$$
mathbb{P}left(
sup_{0 leq tleq T}X_t
geq x
right).
$$

When can a lower-bound be obtained; that is a function of $x$ and $t$ such that
$$
f(t,x)leq mathbb{P}left(
sup_{0 leq tleq T} X_t
geq x
right)?
$$

probability probability-theory large-deviation-theory extreme-value-theorem

share|cite|improve this question

asked Mar 18 at 20:43

AIM_BLBAIM_BLB

2,5392820

$endgroup$

share|cite|improve this question

asked Mar 18 at 20:43

AIM_BLBAIM_BLB

2,5392820

share|cite|improve this question

asked Mar 18 at 20:43

AIM_BLBAIM_BLB

2,5392820

asked Mar 18 at 20:43

AIM_BLBAIM_BLB

2,5392820

asked Mar 18 at 20:43

AIM_BLBAIM_BLB

2,5392820