Approximating Countable Markov Chains |
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Page 74
... construction of ƒ on { C and t≤ 1 } proceeds as in the special case , and will not be considered again . The construction of ƒ on { D and < 1 } is harder . By quasiregularity , X ( t + ) = q - lim , 10 X ( t + t ) exists in Ï . For he ...
... construction of ƒ on { C and t≤ 1 } proceeds as in the special case , and will not be considered again . The construction of ƒ on { D and < 1 } is harder . By quasiregularity , X ( t + ) = q - lim , 10 X ( t + t ) exists in Ï . For he ...
Page 86
... construction = = [ ( PG ) F ] p ( 69 ) = ( PF ) p ( 65 ) or ( 1.35 ) . = Now ( 56 ) forces ( 68 ) . Relation ( 68 ) ... construction . By ( 65 ) , Yn = ( Yn + 1 ) Fn On some convenient triple , construct a Markov chain Z with stationary ...
... construction = = [ ( PG ) F ] p ( 69 ) = ( PF ) p ( 65 ) or ( 1.35 ) . = Now ( 56 ) forces ( 68 ) . Relation ( 68 ) ... construction . By ( 65 ) , Yn = ( Yn + 1 ) Fn On some convenient triple , construct a Markov chain Z with stationary ...
Page 120
... construction , c , must tend to 0 rapidly . This leads to the conjecture that lim P ' ( t , i , i ) = ∞ for most approaches of t to 0. One formalization would be that P ' ( t , i , i ) is approximately continuous at t = 0. Another ...
... construction , c , must tend to 0 rapidly . This leads to the conjecture that lim P ' ( t , i , i ) = ∞ for most approaches of t to 0. One formalization would be that P ' ( t , i , i ) is approximately continuous at t = 0. Another ...
Contents
RESTRICTING THE RANGE | 1 |
RESTRICTING THE RANGE APPLICATIONS | 64 |
CONSTRUCTING THE GENERAL MARKOV CHAIN | 95 |
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1)-intervals a₁ absorbing Approximating Countable Markov argue argument b₂ binary rationals Brownian Motion chapter coincides conditional distribution construction converges defined exponentially distributed F(1)-measurable Figure finite subset Fubini holding i₁ implies In+1 independent and exponential infinite interval of constancy joint distribution jump Lebesgue measure Lebesgue s:0 Lemma Let f locally finitary Markov chain Markov process Markov property Markov with stationary Markov with transitions Math nondecreasing notation null set P-distribution P-probability Poisson process Poisson with parameter positive Prob probability triple product measurable prove pseudo-jumps Qn(i Qn(j Qn+1 quasiregular random variables recurrent restriction retracted right continuous sample functions satisfies Section sequence standard stochastic semigroup starting stationary standard transitions stationary transitions strictly increasing Suppose T₁ Theorem TJ,n tj,o visits VOLKER STRASSEN WILLIAM FELLER X-time corresponding XN+1 YN+m Z₁