Time Development of Explosion of Stochastic Process with Repulsive Drift of Polynomial Growth

Journal Article · Wed Jun 18 00:00:00 EDT 2008 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.2956800· OSTI ID:21148827

Nakamura, Toru ^[1]; Ezawa, Hiroshi ^[2]; Watanabe, Keiji ^[3]

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1. Department of Mathematics, Sundai Preparatory School, Kanda-Surugadai, Chiyoda-ku, Tokyo 101-0062 (Japan)
2. Department of Physics, Gakushuin University, Mejiro, Toshima-ku, Tokyo 171-8588 (Japan)
3. Department of Physics, Meisei University, Hino, Tokyo 191-8506 (Japan)

For a diffusion process X(t) representing the momentum of a particle subject to an external force f(x) and a random force dB(t)/dt in one-dimensional space, almost all sample paths explode to infinity in finite times if f(x) grows repulsively to infinity faster than linear as |x|{yields}{infinity}, so that the survival probability P(t) of the particle by time t decreases to zero as time passes. It is shown that P(t) decays at least exponentially in time and the rate of the exponential decay is strictly positive and equal to the lowest eigenvalue of a Hamiltonian of an imaginary-time Schroedinger equation.

• OSTI ID: 21148827
• Journal Information: AIP Conference Proceedings, Vol. 1021, Issue 1; Conference: 5. Jagna international workshop on stochastic and quantum dynamics of biomolecular systems, Jagna, Bohol (Philippines), 3-5 Jan 2008; Other Information: DOI: 10.1063/1.2956800; (c) 2008 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIFFUSION
EIGENVALUES
HAMILTONIANS
NOISE
ONE-DIMENSIONAL CALCULATIONS
POLYNOMIALS
PROBABILITY
QUANTUM MECHANICS
RANDOMNESS
SCHROEDINGER EQUATION
SPACE
STOCHASTIC PROCESSES