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First Passage Time Derivation for Wave Perturbation by
Skew Brownian Motion
Siti Noranisa Seiril Emyza
Supervisor: Dr. Ilyani Binti Abdullah
Bachelor of Science (Financial Mathematics)
School of Informatics and Applied Mathematics
The skew Brownian motion behaves like Brownian motion except use an independent
Bernoulli random variable of parameter p to choose the sign of each excursion. This study
was conducted to determine the derivation of first passage time using the skew Brownian
motion method. The derivation of the first passage time is used to determine the effect
of perturbation on the movement of the ocean waves. The skew Brownian motion is
constructed with consideration of one-dimensional Brownian motion. The transition
probability density function of skew Brownian motion is solved using the fundamental
solution of the absorbing boundary to obtain the derivation of the first passage time. As
a result, the first passage time can be formed using the skew Brownian motion method.
Therefore, the time taken by a sea wave to approach the endpoint with the presence of
disturbance can be determined by this derivation.
887 | UMT UNDERGRADUATE RESEARCH DAY 2018