scholarly journals Probability distribution of the boundary local time of reflected Brownian motion in Euclidean domains

2019 ◽  
Vol 100 (6) ◽  
Author(s):  
Denis S. Grebenkov
Keyword(s):  
Brownian Motion ◽  
Probability Distribution ◽  
Local Time ◽  
Reflected Brownian Motion ◽  
Euclidean Domains

Moderate deviation principle for multivalued stochastic differential equations

2019 ◽  
Vol 20 (03) ◽  
pp. 2050015 ◽  
Author(s):  
Hua Zhang
Keyword(s):  
Brownian Motion ◽  
Weak Convergence ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Moderate Deviation ◽  
Reflected Brownian Motion ◽  
Moderate Deviation Principle ◽  
Deviation Principle ◽  
Weak Convergence Approach

In this paper, we prove a moderate deviation principle for the multivalued stochastic differential equations whose proof are based on recently well-developed weak convergence approach. As an application, we obtain the moderate deviation principle for reflected Brownian motion.

Self-avoiding random walk: A Brownian motion model with local time drift

1987 ◽  
Vol 74 (2) ◽  
pp. 271-287 ◽  
Author(s):  
J. R. Norris ◽  
L. C. G. Rogers ◽  
David Williams
Keyword(s):  
Brownian Motion ◽  
Random Walk ◽  
Local Time ◽  
Motion Model ◽  
Time Drift ◽  
Brownian Motion Model

Pricing path-dependent options in a Black-Scholes market from the distribution of homogeneous Brownian functionals

2004 ◽  
Vol 41 (01) ◽  
pp. 1-18
Author(s):  
T. Fujita ◽  
F. Petit ◽  
M. Yor
Keyword(s):  
Brownian Motion ◽  
Local Time ◽  
Black Scholes ◽  
Explicit Formulae ◽  
Path Dependent

We give some explicit formulae for the prices of two path-dependent options which combine Brownian averages and penalizations. Because these options are based on both the maximum and local time of Brownian motion, obtaining their prices necessitates some involved study of homogeneous Brownian functionals, which may be of interest in their own right.

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