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Conditioning an additive functional of a Markov chain to stay nonnegative. I. Survival for a long time
| Content Provider | Scilit |
|---|---|
| Author | Jacka, Saul D. Lazic, Zorana Warren, Jon |
| Copyright Year | 2005 |
| Description | Let (X t ) t≥0 be a continuous-time irreducible Markov chain on a finite state space E, let v be a map v: E→ℝ\{0}, and let (φ t ) t≥0 be an additive functional defined by φ t $=∫_{0}$ t v(X s )d s. We consider the case in which the process (φ t ) t≥0 is oscillating and that in which (φ t ) t≥0 has a negative drift. In each of these cases, we condition the process (X t ,φ t ) t≥0 on the event that (φ t ) t≥0 is nonnegative until time T and prove weak convergence of the conditioned process as T→∞. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/2E6238C63933D25F28757A495EFCED8C/S0001867800000641a.pdf/div-class-title-conditioning-an-additive-functional-of-a-markov-chain-to-stay-nonnegative-i-survival-for-a-long-time-div.pdf |
| Ending Page | 1034 |
| Page Count | 20 |
| Starting Page | 1015 |
| ISSN | 00018678 |
| e-ISSN | 14756064 |
| DOI | 10.1017/s0001867800000641 |
| Journal | Advances in Applied Probability |
| Issue Number | 04 |
| Volume Number | 37 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2005-12-01 |
| Access Restriction | Open |
| Subject Keyword | Advances in Applied Probability Markov Chain Conditional Law Weak Convergence |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Statistics and Probability |
