Dirichlet boundary conditions for a class of non-Markovian Gaussian stochastic processes

  • Christopher C. Bernido University of San Carlos, Cebu City and Research Center for Theoretical Physics, Central Visayan Institute Foundation, Jagna, Bohol
  • Karl Patrick Casas University of San Carlos and Cebu Normal University, Cebu City
  • Ma. Victoria Carpio-Bernido University of San Carlos, Cebu City and Research Center for Theoretical Physics, Jagna, Bohol


Varying conditions at boundaries can give rise to interesting effects on a stochastic system. For example, the first passage time of a non-Markovian stochastic process with boundaries has many practical applications. In this talk, we consider a class of non-Markovian white noise processes that has recently been applied to various complex systems ranging in size from nanoscales to gigameters. The probability density function (PDF) under Dirichlet conditions for this class of stochastic processes with memory is evaluated in closed form using white noise analysis. The PDF that vanishes at a boundary is then used to calculate physically interesting properties such as the survival probability and first passage time of fluctuating observables. In particular, we obtain the first passage time density for stochastic processes with different types of memory behavior.

About the Speaker

Christopher C. Bernido is presently the President of the Central Visayan Institute Foundation (CVIF). He obtained his Ph.D. (Physics) in 1982 and M.S. (Physics) in 1979 from the State University of New York at Albany, USA, and B.S. (Physics) degree from the University of the Philippines (UP) at Diliman in 1977. He was conferred the degrees Doctor of Humanities (honoris causa) by the Holy Angel University (2012) and Doctor of Pedagogy (honoris causa) by Ateneo de Naga University (2014).
Chris was a Research Fellow of the Alexander von Humboldt Foundation in Germany from 1987 to 1989. From 1996 to 2001, he was also a Senior Associate Member of the International Centre for Theoretical Physics in Trieste, Italy.
Chris taught for 17 years at UP Diliman where he got the Chancellor's Award for Outstanding Researcher and Teacher in 1995. He was the Director of the National Institute of Physics in UP from 1983-1986, and served as President of the Samahang Pisika ng Pilipinas (SPP, Physics Society of the Philippines) from 1984-1987. He received in 1987 the Achievement Award in Physics from the National Research Council of the Philippines. He is the founding Director of the Research Center for Theoretical Physics, CVIF, which has organized nine international workshops in Jagna, Bohol, with Proceedings published by the American Institute of Physics (New York) and World Scientific (Singapore). He was elected member of the National Academy of Science and Technology of the Philippines in 2007. In 2016, he was elected Fellow of the SPP.
Together with his wife Maria Victoria, they were awarded the Ramon Magsaysay Award in 2010 for improving basic education in the Philippines through their CVIF Dynamic Learning Program.

How to Cite
C. Bernido, K. P. Casas, and M. V. Carpio-Bernido. Dirichlet boundary conditions for a class of non-Markovian Gaussian stochastic processes, Proceedings of the Samahang Pisika ng Pilipinas 38, SPP-2020-INV-3F-01 (2020). URL: https://paperview.spp-online.org/proceedings/article/view/SPP-2020-INV-3F-01.