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

• Published in: AIP conference proceedings Vol. 1021; no. 1; pp. 46 - 56
• Main Authors: Nakamura, Toru, Ezawa, Hiroshi, Watanabe, Keiji
• Format: Journal Article
• Language: English
• Published: United States 01.01.2008
• Subjects: CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DIFFUSION; EIGENVALUES; HAMILTONIANS; NOISE; ONE-DIMENSIONAL CALCULATIONS; POLYNOMIALS; PROBABILITY; QUANTUM MECHANICS; RANDOMNESS; SCHROEDINGER EQUATION; SPACE; STOCHASTIC PROCESSES

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|'[, so that the...