scholarly journals Sharp Large Deviation for the Energy of -Brownian Bridge

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Shoujiang Zhao ◽  
Qiaojing Liu ◽  
Fuxiang Liu ◽  
Hong Yin
Keyword(s):  
Large Deviation ◽  
Brownian Bridge ◽  
Sharp Large Deviation

Approximate exit probabilities for a Brownian bridge on a short time interval, and applications

1989 ◽  
Vol 21 (1) ◽  
pp. 1-19 ◽  
Author(s):  
H. R. Lerche ◽  
D. Siegmund
Keyword(s):  
Virial Coefficient ◽  
Large Deviation ◽  
Brownian Bridge ◽  
Exit Time ◽  
Second Virial Coefficient ◽  
Dimensional Euclidean Space ◽  
Time Interval ◽  
Short Time Interval ◽  
First Exit Time ◽  
Short Time

Let T be the first exit time of Brownian motion W(t) from a region ℛ in d-dimensional Euclidean space having a smooth boundary. Given points ξ0 and ξ1 in ℛ, ordinary and large-deviation approximations are given for Pr{T < ε |W(0) = ξ0, W(ε) = ξ 1} as ε → 0. Applications are given to hearing the shape of a drum and approximating the second virial coefficient.

scholarly journals Rare Events and Conditional Events on Random Strings

2004 ◽  
Vol Vol. 6 no. 2 ◽  
Author(s):  
Mireille Régnier ◽  
Alain Denise
Keyword(s):  
Large Deviation ◽  
Probability Model ◽  
Rare Event ◽  
Bernoulli Model ◽  
Single Word ◽  
Tail Distribution ◽  
A Genome ◽  
International Audience ◽  
Conditional Events ◽  
Sharp Large Deviation

International audience Some strings -the texts- are assumed to be randomly generated, according to a probability model that is either a Bernoulli model or a Markov model. A rare event is the over or under-representation of a word or a set of words. The aim of this paper is twofold. First, a single word is given. One studies the tail distribution of the number of its occurrences. Sharp large deviation estimates are derived. Second, one assumes that a given word is overrepresented. The distribution of a second word is studied; formulae for the expectation and the variance are derived. In both cases, the formulae are accurate and actually computable. These results have applications in computational biology, where a genome is viewed as a text.

scholarly journals MOST-LIKELY-PATH IN ASIAN OPTION PRICING UNDER LOCAL VOLATILITY MODELS

2018 ◽  
Vol 21 (05) ◽  
pp. 1850029 ◽  
Author(s):  
LOUIS-PIERRE ARGUIN ◽  
NIEN-LIN LIU ◽  
TAI-HO WANG
Keyword(s):  
Large Deviation ◽  
Time Window ◽  
Brownian Bridge ◽  
Option Price ◽  
Transition Density ◽  
Small Time ◽  
Option Prices ◽  
Local Volatility ◽  
Volatility Models ◽  
Time Price

This paper addresses the problem of approximating the price of options on discrete and continuous arithmetic averages of the underlying, i.e. discretely and continuously monitored Asian options, in local volatility models. A “path-integral”-type expression for option prices is obtained using a Brownian bridge representation for the transition density between consecutive sampling times and a Laplace asymptotic formula. In the limit where the sampling time window approaches zero, the option price is found to be approximated by a constrained variational problem on paths in time-price space. We refer to the optimizing path as the most-likely path (MLP). An approximation for the implied normal volatility follows accordingly. The small-time asymptotics and the existence of the MLP are also rigorously recovered using large deviation theory.

Approximate exit probabilities for a Brownian bridge on a short time interval, and applications

1989 ◽  
Vol 21 (01) ◽  
pp. 1-19 ◽  
Author(s):  
H. R. Lerche ◽  
D. Siegmund
Keyword(s):  
Virial Coefficient ◽  
Large Deviation ◽  
Brownian Bridge ◽  
Exit Time ◽  
Second Virial Coefficient ◽  
Dimensional Euclidean Space ◽  
Time Interval ◽  
Short Time Interval ◽  
First Exit Time ◽  
Short Time

LetTbe the first exit time of Brownian motionW(t) from a region ℛ ind-dimensional Euclidean space having a smooth boundary. Given points ξ0and ξ1in ℛ, ordinary and large-deviation approximations are given for Pr{T &lt; ε|W(0) = ξ0,W(ε)=ξ1} asε→ 0. Applications are given to hearing the shape of a drum and approximating the second virial coefficient.

scholarly journals Sharp large deviations for some hyperbolic systems

2013 ◽  
Vol 35 (1) ◽  
pp. 249-273 ◽  
Author(s):  
VESSELIN PETKOV ◽  
LUCHEZAR STOYANOV
Keyword(s):  
Large Deviations ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Hyperbolic Systems ◽  
Axiom A ◽  
Deviation Principle ◽  
Basic Set ◽  
Sharp Large Deviations ◽  
Additional Regularity ◽  
Sharp Large Deviation

AbstractWe prove a sharp large deviation principle concerning intervals shrinking with sub-exponential speed for certain models involving the Poincaré map related to a Markov family for an Axiom A flow restricted to a basic set $\Lambda $ satisfying some additional regularity assumptions.

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