A comparison theorem for conditioned Markov processes

1991 ◽  
Vol 28 (01) ◽  
pp. 74-83 ◽  
Author(s):  
G. O. Roberts
Keyword(s):  
Markov Processes ◽  
Comparison Theorem ◽  
Hitting Time ◽  
Time Dependent ◽  
One Dimensional

Intuitively, the effect of conditioning a one-dimensional process to remain below a certain (possibly time-dependent) boundary is to ‘push' the process downwards. This paper investigates the effect of such conditioning, and finds the class of processes for which our intuition is accurate. It is found that ordinary stochastic inequalities are in general unsuitable for making statements about such conditioned processes, and that a stronger type of inequality is more appropriate. The investigation is motivated by applications in estimation of boundary hitting time distributions.

A comparison theorem for conditioned Markov processes

1991 ◽  
Vol 28 (1) ◽  
pp. 74-83 ◽  
Author(s):  
G. O. Roberts
Keyword(s):  
Markov Processes ◽  
Comparison Theorem ◽  
Hitting Time ◽  
Time Dependent ◽  
One Dimensional

Intuitively, the effect of conditioning a one-dimensional process to remain below a certain (possibly time-dependent) boundary is to ‘push' the process downwards. This paper investigates the effect of such conditioning, and finds the class of processes for which our intuition is accurate. It is found that ordinary stochastic inequalities are in general unsuitable for making statements about such conditioned processes, and that a stronger type of inequality is more appropriate.The investigation is motivated by applications in estimation of boundary hitting time distributions.

scholarly journals Hamiltonian Approach to Magnetic Fields with Toroidal Surfaces

1985 ◽  
Vol 40 (10) ◽  
pp. 959-967
Author(s):  
A. Salat
Keyword(s):  
Magnetic Field ◽  
Hamiltonian System ◽  
Magnetic Fields ◽  
Constant Pressure ◽  
Time Dependent ◽  
Hamiltonian Approach ◽  
One Dimensional ◽  
Mhd Equilibrium ◽  
Magnetic Surfaces ◽  
Rotational Transform

The equivalence of magnetic field line equations to a one-dimensional time-dependent Hamiltonian system is used to construct magnetic fields with arbitrary toroidal magnetic surfaces I = const. For this purpose Hamiltonians H which together with their invariants satisfy periodicity constraints have to be known. The choice of H fixes the rotational transform η(I). Arbitrary axisymmetric fields, and nonaxisymmetric fields with constant η(I) are considered in detail.Configurations with coinciding magnetic and current density surfaces are obtained. The approach used is not well suited, however, to satisfying the additional MHD equilibrium condition of constant pressure on magnetic surfaces.

A time-dependent model for high-pressure discharges in narrow ablative capillaries

1993 ◽  
Vol 50 (1) ◽  
pp. 51-70 ◽  
Author(s):  
D. Zoler ◽  
S. Cuperman ◽  
J. Ashkenazy ◽  
M. Caner ◽  
Z. Kaplan
Keyword(s):  
High Pressure ◽  
Equation Of State ◽  
Time Dependent ◽  
Dimensional Model ◽  
Plasma Sources ◽  
One Dimensional ◽  
Space And Time ◽  
Dependent Model ◽  
Energy Equations ◽  
Time Dependent Model

A time-dependent quasi-one-dimensional model is developed for studying high- pressure discharges in ablative capillaries used, for example, as plasma sources in electrothermal launchers. The main features of the model are (i) consideration of ablation effects in each of the continuity, momentum and energy equations; (ii) use of a non-ideal equation of state; and (iii) consideration of space- and time-dependent ionization.

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