Diffusion processes on an open time interval and their time reversal

  • Masao Nagasawa
  • Thomas Domenig


To discuss time reversal of (Schrödinger’s) diffusion processes, which are in general time-inhomogeneous, they must be defined on a closed time interval [a, b], −∞ < a <b <∞, because prescribed initial and terminal distributions μ a and μ b at t = a, and b, respectively, are involved. If a diffusion process is given only on an open time interval (a, b), we must first consider the process on a closed time interval [a′, b′], a < a′ <b ′ < b, and then analyze the limiting behaviour of the process as a ′ ↓ a, and b′b. This requires closer analysis of stochastic differential equations in connection with time reversal. In this context, a Skorokhod problem with singular drift is discussed.


Brownian Motion Diffusion Process Stochastic Differential Equation Closed Time Interval Time Reversal 
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Copyright information

© Springer-Verlag Tokyo 1996

Authors and Affiliations

  • Masao Nagasawa
    • 1
  • Thomas Domenig
    • 1
  1. 1.Institut für MathematikUniversität ZürichZürichSwitzerland

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