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- Title
Martingales associated with functions of Markov and finite variation processes.
- Authors
Kella, Offer
- Abstract
It is emphasized that HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>X</mi><mi>s</mi></msub></math> ht (not HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>X</mi><mrow><mi>s</mi><mo>-</mo></mrow></msub></math> ht ) appears in both HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>f</mi><mo stretchy="false">(</mo><msub><mi>X</mi><mi>s</mi></msub><mo>,</mo><msub><mi>Y</mi><mi>s</mi></msub><mo stretchy="false">)</mo></mrow></math> ht and HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>f</mi><mo stretchy="false">(</mo><msub><mi>X</mi><mi>s</mi></msub><mo>,</mo><msub><mi>Y</mi><mrow><mi>s</mi><mo>-</mo></mrow></msub><mo stretchy="false">)</mo></mrow></math> ht in the sum on the right-hand side. Under some further (usually) easily verifiable conditions, it was shown that in fact HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>M</mi><mi>t</mi></msub></math> ht is a square integrable martingale which behaves nicely as a function of I t i both in the almost sure sense and in the HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>L</mi><mn>2</mn></msup></math> ht sense.
- Subjects
MARTINGALES (Mathematics); MARKOV processes; QUEUING theory; STOCHASTIC processes; LEVY processes; FINITE, The
- Publication
Queueing Systems, 2022, Vol 100, Issue 3/4, p205
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-022-09749-8